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＜電子ブック＞
Mean Oscillations and Equimeasurable Rearrangements of Functions / by Anatolii A. Korenovskii
(Lecture Notes of the Unione Matematica Italiana. ISSN:18629121 ; 4)

版	1st ed. 2007.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	VIII, 189 p : online resource
著者標目	*Korenovskii, Anatolii A author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Fourier analysis LCSH:Functional analysis FREE:Analysis FREE:Fourier Analysis FREE:Functional Analysis
一般注記	Preface -- 1.Preliminaries and auxilliary results -- 2. Properties of oscillations and the definition of the BMO-class -- 3.Estimates of rearrangements and the John-Nirenberg theorem -- 4.The BMO-estimates of the Hardy-type transforms -- 5.The Gurov-Reshetnyak class of functions -- Appendix: A.The boundedness of the Hardy-Littlewood maximal operator from BMO into BLO -- B.The weighted analogs of the Riesz lemma and the Gurov-Reshetnyak theorem -- C.Classes of functions satisfying the reverse Hölder inequality -- References -- Index Various applications of equimeasurable function rearrangements to the ''best constant"-type problems are considered in this volume. Several classical theorems are presented along with some very recent results. In particular, the text includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation (BMO) functions with sharp exponent, a refinement of the Gurov-Reshetnyak lemma, sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, reverse Hölder, and Gehring classes, etc. This volume is interesting for graduate students and mathematicians involved with these topics. HTTP:URL=https://doi.org/10.1007/978-3-540-74709-3

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