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Mean Oscillations and Equimeasurable Rearrangements of Functions de Anatolii A. Korenovskii

Mean Oscillations and Equimeasurable Rearrangements of Functions: Lecture Notes of the Unione Matematica Italiana, cartea 4

Autor Anatolii A. Korenovskii
en Limba Engleză Paperback – 19 sep 2007
Considers various applications of equimeasurable function rearrangements to the "best constant"- type problems. This volume 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, and Gurov-Reshetnyak, reverse Holder.
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Specificații

ISBN-13: 9783540747086
ISBN-10: 3540747087
Pagini: 200
Ilustrații: VIII, 189 p.
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.31 kg
Ediția:2007
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes of the Unione Matematica Italiana

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.

Recenzii

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)

Textul de pe ultima copertă

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.
 

Caracteristici

Includes supplementary material: sn.pub/extras