Mean Oscillations and Equimeasurable Rearrangements of Functions
Published on 19. September 2007
Book
Paperback/Softback
VIII, 189 pages
978-3-540-74708-6 (ISBN)
Description
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.
Reviews / Votes
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)
More details
Series
Edition
2007 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 189 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
640 gr
ISBN-13
978-3-540-74708-6 (9783540747086)
DOI
10.1007/978-3-540-74709-3
Schweitzer Classification
Other editions
Additional editions
Anatolii A. Korenovskii
Mean Oscillations and Equimeasurable Rearrangements of Functions
E-Book
09/2007
Springer
€35.30
Available for download
Content
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.