Nicola Arcozzi'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

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

Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

By: Donatella Danielli,Nicola Garofalo,Duy-Minh Nhieu

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Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

By: Donatella Danielli,Nicola Garofalo,Duy-Minh Nhieu

The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Caratheodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on a lower dimensional manifold, and which satisfies an Ahlfors type condition with respect to the standard Lebesgue measure. We also study the extension problem for the relevant Besov spaces. Various concrete applications to the setting of Carnot groups are analyzed in detail and an application to the solvability of the subelliptic Neumann problem is presented.

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Page Count

138

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082183911X

ISBN 13

9780821839119

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

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

559

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450828

ISBN 13

9781470450823

Book's by Nicola Arcozzi

The Dirichlet Space and Related Function Spaces

The Dirichlet Space and Related Function Spaces

Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Caratheodory Spaces

The Dirichlet Space and Related Function Spaces

The Dirichlet Space and Related Function Spaces

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