Mean Oscillations and Equimeasurable Rearrangements of Functions
Title:
Mean Oscillations and Equimeasurable Rearrangements of Functions
Author:
Korenovskii, Anatolii. author.
ISBN:
9783540747093
Personal Author:
Physical Description:
VIII, 189 p. online resource.
Series:
Lecture Notes of the Unione Matematica Italiana, 4
Contents:
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.
Abstract:
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. .
Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/978-3-540-74709-3