Mean Oscillations and Equimeasurable Rearrangements of Functions - Lecture Notes of the Unione Matematica Italiana 4 (Paperback)Anatolii Korenovskii (author)
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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.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Number of pages: 189
Weight: 640 g
Dimensions: 235 x 155 x 10 mm
Edition: 2007 ed.
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)