Anatolii Korenovskii, "Mean Oscillations and Equimeasurable Rearrangements of Functions"
Springer; 1 edition (October 2007) | ISBN: 3540747087 | 189 pages | PDF | 1,6 Mb
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.