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 H?lder, and Gehring classes, etc. This volume is interesting for graduate students and mathematicians involved with these topics.
Lecture Notes of the Unione Matematica Italiana
4
Editorial Board
Franco Brezzi (Editor in Chief) Dipartimento di Matematica Universita di Pavia Via Ferrata I 27100 Pavia, Italy e-mail:
[email protected] John M. Ball Mathematical Institute 24-29 St Giles’ Oxford OX1 3LB United Kingdom e-mail:
[email protected] Alberto Bressan Department of Mathematics Penn State University University Park State College PA 16802, USA e-mail:
[email protected] Fabrizio Catanese Mathematisches Institut Universitatstraße 30 95447 Bayreuth, Germany e-mail:
[email protected] Carlo Cercignani Dipartimento di Matematica Politecnico di Milano Piazza Leonardo da Vinci 32 20133 Milano, Italy