Eric T. Sawyer's Books

The Dirichlet Space and Related Function Spaces

By: Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick

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The Dirichlet Space and Related Function Spaces

By: Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick

The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

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Page Count

559

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450828

ISBN 13

9781470450823

Holder Continuity of Weak Solutions to Subelliptic Equations with Rough Coefficients

By: Eric T. Sawyer,Richard L. Wheeden

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Holder Continuity of Weak Solutions to Subelliptic Equations with Rough Coefficients

By: Eric T. Sawyer,Richard L. Wheeden

This mathematical monograph is a study of interior regularity of weak solutions of second order linear divergence form equations with degenerate ellipticity and rough coefficients. The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are H lder continuous. They present two types of results f

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Page Count

176

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838261

ISBN 13

9780821838266

Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

By: Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer

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Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

By: Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer

Contents: A tree structure for the unit ball $mathbb B? n$ in $mathbb C'n$; Carleson measures; Pointwise multipliers; Interpolating sequences; An almost invariant holomorphic derivative; Besov spaces on trees; Holomorphic Besov spaces on Bergman trees; Completing the multiplier interpolation loop; Appendix; Bibliography

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Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839179

ISBN 13

9780821839171

Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

By: Yongsheng Han,Eric T. Sawyer

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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

By: Yongsheng Han,Eric T. Sawyer

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

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Page Count

138

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821825925

ISBN 13

9780821825921

Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

By: Lyudmila Korobenko,Cristian Rios,Eric Sawyer,Ruipeng Shen

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Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

By: Lyudmila Korobenko,Cristian Rios,Eric Sawyer,Ruipeng Shen

View the abstract: https://bookstore.ams.org/memo-269-1311/

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Page Count

130

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470444011

ISBN 13

9781470444013

Book's by Eric T. Sawyer

The Dirichlet Space and Related Function Spaces

The Dirichlet Space and Related Function Spaces

Holder Continuity of Weak Solutions to Subelliptic Equations with Rough Coefficients

Holder Continuity of Weak Solutions to Subelliptic Equations with Rough Coefficients

Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

Local Boundedness, Maximum Principles, and Continuity of Solutions to Infinitely Degenerate Elliptic Equations with Rough Coefficients

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