Anatolii Korenovskii

Mean Oscillations and Equimeasurable Rearrangements of Functions

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Lecture Notes of the Unione Matematica Italiana 4
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-74708-6
• Seitenzahl: 189
• Englisch
• Abmessung: 235mm x 157mm
• Gewicht: 332g
• ISBN-13: 9783540747086
• ISBN-10: 3540747087
• Artikelnr.: 23109445

Inhaltsangabe

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.

Rezensionen

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)