Weighted norm inequalities for integral transforms with product kernels / Vakhtang Kokilashvili, Alexander Meskhi and Lars-Erik Persson.

Format:

Book

Author/Creator:

Kokilashvili, V. M. (Vakhtang Mikhaĭlovich)

Contributor:

Meskhi, Alexander.

Persson, Lars-Erik, 1944-

Series:

Mathematics research developments series.

Mathematics research developments series

Language:

English

Subjects (All):

Inequalities (Mathematics).

Integral transforms.

Physical Description:

1 online resource (358 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2010.

Language Note:

English

Summary:

A systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. The considered product kernels cover that case when factors of kernels have essential (less than one) singularities.

Contents:

Intro

WEIGHTED NORM INEQUALITIES FOR INTEGRAL TRANSFORMS WITH PRODUCT KERNELS

Contents

Preface

Acknowledgment

Basic Notation

Hardy and P´olya-Knopp Inequalities

1.1 A Two-dimensional Hardy-type Inequality

1.2 The Two-dimensional P´olya-Knopp Type Inequality

1.3 The Multidimensional Case: 1&lt

p q&lt

1

1.4 The Multidimensional Case: 1&lt

q&lt

p&lt

1.5 Multidimensional P´olya-Knopp Type Inequalities

1.6 Double Riemann-Liouville Transform Without Sin-gularity

1.7 Further Results

1.8 Notes and Comments on Chapter 1

Weighted Boundedness Criteria for Integral Transforms With Product Kernels

2.1 Integrals with General Product Kernels

2.2 Truncated Potentials and Ball Fractional Integrals

2.3 The Case of m-Multiple Kernels

2.4 Multiple One-sided Potentials.Trace Inequality

2.5 Multidimensional Hardy-Type Inequalities with General Kernels Via Convexity

2.6 Weighted Integral Inequalities for Monotonic Func-tions, the Case p q

2.7 Weighted Integral Inequalities for Monotonic Functions, the Case 0&lt

2.8 Further Results and Applications

2.9 Notes and Comments on Chapter 2.

One-sided Fractional Multiple Operators

3.1 One-dimensional Operators

3.2 One-sided Strong Fractional Maximal Functions

3.3 Mixed-type Operators

3.4 One-sided Potentials with Product Kernels

3.5 One-weight Inequalities

3.6 Weighted Strichartz Estimates for Semilinear Wave Equations

3.7 Notes and Comments on Chapter 3

Strong Fractional Maximal Functions and Multiple Riesz Potentials

4.1 Single Kernel Operators

4.2 Two-weight Problem for Strong Fractional Maxi-mal Functions

4.3 Mixed Multiple Operators

4.4 Solution of the Trace Problem.

4.5 Riesz Potentials with Product Kernels

4.6 Some Remarks

4.7 Notes and Comments on Chapter 4

Strong Maximal Functions and Hilbert Transforms with Product Kernels

5.1 Single Maximal Functions

5.2 Strong Maximal Functions

5.3 Two-weight Estimates for Hilbert Transforms with Single Kernel

5.4 Hilbert Transforms with Product Kernels

The Case of Increasing Weights

The Case of Other Type of Weights

The n-dimensional Case

5.5 Examples

5.6 Applications to the Fourier Multipliers

5.7 Notes and Comments on Chapter 5

Two-weight Estimates for Fourier Operators and Bernstein Inequalities

6.1 Two-weight Inequalities for Ces`aro and Abel-Poi-sson Means of Fourier Series

6.2 On the Means of Fourier Integrals

6.3 Bernstein Inequalities in the Two-weighted Setting

6.4 Notes and Comments on Chapter 6

Appendix: Multidimensional Lorentz Spaces

Open Problems

Bibliography

INDEX.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

1-61324-612-9

OCLC:

742353849