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.
Rezensionen / Stimmen
From the reviews:
"This book is devoted to classes (spaces) of functions that can be described in terms of mean oscillations. . The sharp constants in the corresponding relations have been found in a number of works by the author of the book under review and his students; these works form the core of the present book. . The book is well written. We mention that it contains many examples with full and very careful calculations. . a good and convenient source for anyone interested in the area." (Andrei K. Lerner, Mathematical Reviews, Issue 2008 k)
Reihe
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Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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Dateigröße
ISBN-13
978-3-540-74709-3 (9783540747093)
DOI
10.1007/978-3-540-74709-3
Schweitzer Klassifikation
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.
