TY  - BOOK
AU  - Korenovskii,Anatolii
ED  - SpringerLink (Online service)
TI  - Mean Oscillations and Equimeasurable Rearrangements of Functions
T2  - Lecture Notes of the Unione Matematica Italiana,
SN  - 9783540747093
AV  - QA299.6-433 
U1  - 515 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Fourier analysis
KW  - Functional analysis
KW  - Analysis
KW  - Fourier Analysis
KW  - Functional Analysis
KW  - Electronic books
KW  - local
N1  - 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
N2  - 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.
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/978-3-540-74709-3
ER  -