Mean Oscillations and Equimeasurable Rearrangements of Functions

  • Anatolii Korenovskii

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 4)

About this book

Introduction

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.

 

Keywords

Gurov – Reshetnyak classes Maximum bounded mean oscillation bounded mean oscillation (BMO) equimeasurable rearrangements of functions mean oscillation reverse Hölder inequalities

Authors and affiliations

  • Anatolii Korenovskii
    • 1
  1. 1.Institute of Mathematics, Economics and MechanicsOdessa National I.I. Mechnikov UniversityOdessaUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74709-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74708-6
  • Online ISBN 978-3-540-74709-3
  • Series Print ISSN 1862-9113
  • About this book