Mean Oscillations and Equimeasurable Rearrangements of Functions [electronic resource] /
Korenovskii, Anatolii A.author.
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. .
Description based upon print version of record.
Includes bibliographical references (p. [183]-186) and index.
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. .
Mathematical analysis.
Analysis (Mathematics).
Fourier analysis.
Functional analysis.
Analysis.
Fourier Analysis.
Functional Analysis.
Lecture Notes of the Unione Matematica Italiana