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Mean Oscillations and Equimeasurable Rearrangements of Functions

By: Korenovskii, Anatolii [author.].
Contributor(s): SpringerLink (Online service)0.
Material type: materialTypeLabelBookSeries: Lecture Notes of the Unione Matematica Italiana: 440Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: VIII, 189 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540747093.Subject(s): Mathematics. 0 | Mathematical analysis. 0 | Analysis (Mathematics). 0 | Fourier analysis. 0 | Functional analysis.14 | Mathematics.24 | Analysis.24 | Fourier Analysis.24 | Functional Analysis.2DDC classification: 515 Online resources: Click here to access online
Contents:
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 H�lder inequality -- References -- Index.
In: Springer eBooks08Summary: 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. . 0
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Item type Current location Call number Status Date due Barcode Item holds
PK Kelkar Library, IIT Kanpur
Available EBK9356
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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 H�lder inequality -- References -- Index.

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. . 0

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