Del 4 - Lecture Notes of the Unione Matematica Italiana

Mean Oscillations and Equimeasurable Rearrangements of Functions

Häftad, Engelska, 2007

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This volume considers various applications of equimeasurable function rearrangements to the "best constant"-type problems. It presents several classical theorems along with some very recent results. Coverage includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation functions with sharp exponent, and sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, and Gehring classes.

Produktinformation

Utgivningsdatum2007-09-19
Mått155 x 235 x 12 mm
Vikt308 g
FormatHäftad
SpråkEngelska
SerieLecture Notes of the Unione Matematica Italiana
Antal sidor189
FörlagSpringer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN9783540747086

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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.

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)