Bounded mean oscillation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Bounded mean oscillation" in English language version.

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Aside with the collected papers of Fritz John, a general reference for the theory of functions of bounded mean oscillation, with also many (short) historical notes, is the noted book by Stein (1993, chapter IV). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
The paper (John 1961) just precedes the paper (John & Nirenberg 1961) in volume 14 of the Communications on Pure and Applied Mathematics. John, F. (1961), "Rotation and strain", Communications on Pure and Applied Mathematics, 14 (3): 391–413, doi:10.1002/cpa.3160140316, MR 0138225, Zbl 0102.17404. John, F.; Nirenberg, L. (1961), "On functions of bounded mean oscillation", Communications on Pure and Applied Mathematics, 14 (3): 415–426, doi:10.1002/cpa.3160140317, hdl:10338.dmlcz/128274, MR 0131498, Zbl 0102.04302.
Elias Stein credits only Fefferman for the discovery of this fact: see (Stein 1993, p. 139). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See his proof in the paper Uchiyama 1982. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018.
See the original paper by Fefferman & Stein (1972), or the paper by Uchiyama (1982) or the comprehensive monograph of Stein (1993, p. 142) for a proof. Fefferman, C.; Stein, E. M. (1972), "H^p spaces of several variables", Acta Mathematica, 129: 137–193, doi:10.1007/BF02392215, MR 0447953, Zbl 0257.46078. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See the paper Garnett & Jones 1978 for the details. Garnett, John. B; Jones, Peter W. (September 1978), "The distance in BMO to L^∞", Annals of Mathematics, Second Series, 108 (2): 373–393, doi:10.2307/1971171, JSTOR 1971171, MR 0506992, Zbl 0358.26010.
See for example Girela (2001, pp. 102–103). Girela, Daniel (2001), "Analytic functions of bounded mean oscillation", in Aulaskari, Rauno (ed.), Complex function spaces, Proceedings of the summer school, Mekrijärvi, Finland, August 30-September 3, 1999, Univ. Joensuu Dept. Math. Rep. Ser., vol. 4, Joensuu: Joensuu University, Department of Mathematics, pp. 61–170, MR 1820090, Zbl 0981.30026.
See reference Stein 1993, p. 180. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
Garnett 2007 Garnett, John B. (2007) [1981], Bounded analytic functions, Graduate Texts in Mathematics, vol. 236 (Revised 1st ed.), Springer, pp. xiv+459, ISBN 978-0-387-33621-3, MR 2261424, Zbl 1106.30001.
See the referenced paper by Garnett & Jones 1982 for a comprehensive development of these themes. Garnett, John. B; Jones, Peter W. (1982), "BMO from Dyadic BMO", Pacific Journal of Mathematics, 99 (2): 351–371, doi:10.2140/pjm.1982.99.351, MR 0658065, Zbl 0516.46021.
See reference Stein 1993, p. 140. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 197. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.

books.google.com

Aside with the collected papers of Fritz John, a general reference for the theory of functions of bounded mean oscillation, with also many (short) historical notes, is the noted book by Stein (1993, chapter IV). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
Elias Stein credits only Fefferman for the discovery of this fact: see (Stein 1993, p. 139). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See the original paper by Fefferman & Stein (1972), or the paper by Uchiyama (1982) or the comprehensive monograph of Stein (1993, p. 142) for a proof. Fefferman, C.; Stein, E. M. (1972), "H^p spaces of several variables", Acta Mathematica, 129: 137–193, doi:10.1007/BF02392215, MR 0447953, Zbl 0257.46078. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 180. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 140. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 197. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.

doi.org

The paper (John 1961) just precedes the paper (John & Nirenberg 1961) in volume 14 of the Communications on Pure and Applied Mathematics. John, F. (1961), "Rotation and strain", Communications on Pure and Applied Mathematics, 14 (3): 391–413, doi:10.1002/cpa.3160140316, MR 0138225, Zbl 0102.17404. John, F.; Nirenberg, L. (1961), "On functions of bounded mean oscillation", Communications on Pure and Applied Mathematics, 14 (3): 415–426, doi:10.1002/cpa.3160140317, hdl:10338.dmlcz/128274, MR 0131498, Zbl 0102.04302.
See his proof in the paper Uchiyama 1982. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018.
Jones, Peter (1980). "Extension Theorems for BMO". Indiana University Mathematics Journal. 29 (1): 41–66. doi:10.1512/iumj.1980.29.29005.
See the original paper by Fefferman & Stein (1972), or the paper by Uchiyama (1982) or the comprehensive monograph of Stein (1993, p. 142) for a proof. Fefferman, C.; Stein, E. M. (1972), "H^p spaces of several variables", Acta Mathematica, 129: 137–193, doi:10.1007/BF02392215, MR 0447953, Zbl 0257.46078. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See the paper Garnett & Jones 1978 for the details. Garnett, John. B; Jones, Peter W. (September 1978), "The distance in BMO to L^∞", Annals of Mathematics, Second Series, 108 (2): 373–393, doi:10.2307/1971171, JSTOR 1971171, MR 0506992, Zbl 0358.26010.
See the referenced paper by Garnett & Jones 1982 for a comprehensive development of these themes. Garnett, John. B; Jones, Peter W. (1982), "BMO from Dyadic BMO", Pacific Journal of Mathematics, 99 (2): 351–371, doi:10.2140/pjm.1982.99.351, MR 0658065, Zbl 0516.46021.

handle.net

hdl.handle.net

The paper (John 1961) just precedes the paper (John & Nirenberg 1961) in volume 14 of the Communications on Pure and Applied Mathematics. John, F. (1961), "Rotation and strain", Communications on Pure and Applied Mathematics, 14 (3): 391–413, doi:10.1002/cpa.3160140316, MR 0138225, Zbl 0102.17404. John, F.; Nirenberg, L. (1961), "On functions of bounded mean oscillation", Communications on Pure and Applied Mathematics, 14 (3): 415–426, doi:10.1002/cpa.3160140317, hdl:10338.dmlcz/128274, MR 0131498, Zbl 0102.04302.

jstor.org

See the paper Garnett & Jones 1978 for the details. Garnett, John. B; Jones, Peter W. (September 1978), "The distance in BMO to L^∞", Annals of Mathematics, Second Series, 108 (2): 373–393, doi:10.2307/1971171, JSTOR 1971171, MR 0506992, Zbl 0358.26010.

projecteuclid.org

See the referenced paper by Garnett & Jones 1982 for a comprehensive development of these themes. Garnett, John. B; Jones, Peter W. (1982), "BMO from Dyadic BMO", Pacific Journal of Mathematics, 99 (2): 351–371, doi:10.2140/pjm.1982.99.351, MR 0658065, Zbl 0516.46021.

worldcat.org

search.worldcat.org

Aside with the collected papers of Fritz John, a general reference for the theory of functions of bounded mean oscillation, with also many (short) historical notes, is the noted book by Stein (1993, chapter IV). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
Elias Stein credits only Fefferman for the discovery of this fact: see (Stein 1993, p. 139). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See the original paper by Fefferman & Stein (1972), or the paper by Uchiyama (1982) or the comprehensive monograph of Stein (1993, p. 142) for a proof. Fefferman, C.; Stein, E. M. (1972), "H^p spaces of several variables", Acta Mathematica, 129: 137–193, doi:10.1007/BF02392215, MR 0447953, Zbl 0257.46078. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 180. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 140. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 197. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.

zbmath.org

Aside with the collected papers of Fritz John, a general reference for the theory of functions of bounded mean oscillation, with also many (short) historical notes, is the noted book by Stein (1993, chapter IV). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
The paper (John 1961) just precedes the paper (John & Nirenberg 1961) in volume 14 of the Communications on Pure and Applied Mathematics. John, F. (1961), "Rotation and strain", Communications on Pure and Applied Mathematics, 14 (3): 391–413, doi:10.1002/cpa.3160140316, MR 0138225, Zbl 0102.17404. John, F.; Nirenberg, L. (1961), "On functions of bounded mean oscillation", Communications on Pure and Applied Mathematics, 14 (3): 415–426, doi:10.1002/cpa.3160140317, hdl:10338.dmlcz/128274, MR 0131498, Zbl 0102.04302.
Elias Stein credits only Fefferman for the discovery of this fact: see (Stein 1993, p. 139). Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See his proof in the paper Uchiyama 1982. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018.
See the original paper by Fefferman & Stein (1972), or the paper by Uchiyama (1982) or the comprehensive monograph of Stein (1993, p. 142) for a proof. Fefferman, C.; Stein, E. M. (1972), "H^p spaces of several variables", Acta Mathematica, 129: 137–193, doi:10.1007/BF02392215, MR 0447953, Zbl 0257.46078. Uchiyama, Akihito (1982), "A constructive proof of the Fefferman-Stein decomposition of BMO(Rⁿ)", Acta Mathematica, 148: 215–241, doi:10.1007/BF02392729, MR 0666111, Zbl 0514.46018. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See the paper Garnett & Jones 1978 for the details. Garnett, John. B; Jones, Peter W. (September 1978), "The distance in BMO to L^∞", Annals of Mathematics, Second Series, 108 (2): 373–393, doi:10.2307/1971171, JSTOR 1971171, MR 0506992, Zbl 0358.26010.
See for example Girela (2001, pp. 102–103). Girela, Daniel (2001), "Analytic functions of bounded mean oscillation", in Aulaskari, Rauno (ed.), Complex function spaces, Proceedings of the summer school, Mekrijärvi, Finland, August 30-September 3, 1999, Univ. Joensuu Dept. Math. Rep. Ser., vol. 4, Joensuu: Joensuu University, Department of Mathematics, pp. 61–170, MR 1820090, Zbl 0981.30026.
See reference Stein 1993, p. 180. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
Garnett 2007 Garnett, John B. (2007) [1981], Bounded analytic functions, Graduate Texts in Mathematics, vol. 236 (Revised 1st ed.), Springer, pp. xiv+459, ISBN 978-0-387-33621-3, MR 2261424, Zbl 1106.30001.
See the referenced paper by Garnett & Jones 1982 for a comprehensive development of these themes. Garnett, John. B; Jones, Peter W. (1982), "BMO from Dyadic BMO", Pacific Journal of Mathematics, 99 (2): 351–371, doi:10.2140/pjm.1982.99.351, MR 0658065, Zbl 0516.46021.
See reference Stein 1993, p. 140. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.
See reference Stein 1993, p. 197. Stein, Elias M. (1993), Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton, NJ: Princeton University Press, pp. xiv+695, ISBN 0-691-03216-5, MR 1232192, OCLC 27108521, Zbl 0821.42001.