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

• Autore: Kokilashvili V. M (Vakhtang Mikhaĭlovich)
• Pubblicazione: New York, : Nova Science Publishers, c2010
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (358 p.)
• Disciplina: 515/.723
• Soggetto topico: Inequalities (Mathematics); Integral transforms
• Altri autori: MeskhiAlexander PerssonLars Erik <1944->
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- WEIGHTED NORM INEQUALITIES FOR INTEGRAL TRANSFORMS WITH PRODUCT KERNELS -- 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< -- p q< -- 1 -- 1.4 The Multidimensional Case: 1< -- q< -- p< -- 1 -- 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< -- q< -- p< -- 1 -- 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.
• Titolo autorizzato: Weighted norm inequalities for integral transforms with product kernels
• ISBN: 1-61324-612-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910812011403321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematics research developments series.