Vakhtang Kokilashvili's Books

Weight Theory for Integral Transforms on Spaces of Homogeneous Type

By: Ioseb Genebashvili,Amiran Gogatishvili,Vakhtang Kokilashvil,Miroslav Krbec

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Weight Theory for Integral Transforms on Spaces of Homogeneous Type

By: Ioseb Genebashvili,Amiran Gogatishvili,Vakhtang Kokilashvil,Miroslav Krbec

This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces.

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Page Count

432

Publisher

CRC Press

Published Date

ISBN 10

0582302951

ISBN 13

9780582302952

Weighted Inequalities In Lorentz And Orlicz Spaces

By: Vakhtang Kokilashvili,Miroslav Krbec

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Weighted Inequalities In Lorentz And Orlicz Spaces

By: Vakhtang Kokilashvili,Miroslav Krbec

This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian.

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Page Count

248

Publisher

World Scientific

Published Date

ISBN 10

9814506281

ISBN 13

9789814506281

Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

By: Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko

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Integral Operators in Non-Standard Function Spaces

Volume 1: Variable Exponent Lebesgue and Amalgam Spaces

By: Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko

This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

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Page Count

585

Publisher

Birkhäuser

Published Date

ISBN 10

3319210157

ISBN 13

9783319210155

Bounded and Compact Integral Operators

By: David E. Edmunds,Vakhtang Kokilashvili,Alexander Meskhi

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Bounded and Compact Integral Operators

By: David E. Edmunds,Vakhtang Kokilashvili,Alexander Meskhi

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. It focuses on integral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes, etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. We provide a list of problems which were open at the time of completion of the book. Audience: The book is aimed at a rather wide audience, ranging from researchers in functional and harmonic analysis to experts in applied mathematics and prospective students.

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Page Count

664

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402006195

ISBN 13

9781402006197

Bounded and Compact Integral Operators

By: David E. Edmunds,Vakhtang Kokilashvili,Alexander Meskhi

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Bounded and Compact Integral Operators

By: David E. Edmunds,Vakhtang Kokilashvili,Alexander Meskhi

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Page Count

664

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402006195

ISBN 13

9781402006197

Book's by Vakhtang Kokilashvili

Weight Theory for Integral Transforms on Spaces of Homogeneous Type

Weight Theory for Integral Transforms on Spaces of Homogeneous Type

Weighted Inequalities In Lorentz And Orlicz Spaces

Weighted Inequalities In Lorentz And Orlicz Spaces

Integral Operators in Non-Standard Function Spaces

Integral Operators in Non-Standard Function Spaces

Bounded and Compact Integral Operators

Bounded and Compact Integral Operators

Bounded and Compact Integral Operators

Bounded and Compact Integral Operators

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