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Boundedness results for operators with singular kernels on distribution spaces / Rodolfo H. Torres.
- Format:
- Book
- Author/Creator:
- Torres, Rodolfo H. (Rodolfo Humberto), 1960- author.
- Series:
- Memoirs of the American Mathematical Society ; Number 442.
- Memoirs of the American Mathematical Society, 0065-9266 ; Number 442
- Language:
- English
- Subjects (All):
- Theory of distributions (Functional analysis).
- Pseudodifferential operators.
- Decomposition method.
- Physical Description:
- 1 online resource (185 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, 1991.
- Language Note:
- English
- Summary:
- Discrete decomposition techniques for spaces for functions or distributions are very useful tools for studying many problems in analysis. In this work, the author uses this type of decomposition, associated with the so-called *p-transform and wavelet-transform theories, to analyse a large class of operators, including pseudodifferential operators, Calderon-Zygmund operators, and other operators with singular kernels. The methods used combine Littlewood-Paley type characterizations of spaces of distributions with certain atomic and molecular decompositions. In this way, the study of operators on most of the classical function spaces - such as Hardy spaces, Besov-Lipschitz spaces, and Sobolev spaces - can be accomplished in a unified manner. The book is written in an expository style that makes it suitable for advanced graduate students in analysis.
- Contents:
- ""Table of Contents""; ""Abstract""; ""Acknowledgments""; ""Notation""; ""Â0. Introduction""; ""Â1. The Atomic Decomposition of the Triebelâ€?Lizorkin spaces""; ""1.1 The homogeneous Triebelâ€?Lizorkin spaces""; ""1.2 The inhomogeneous Triebelâ€?Lizorkin spaces""; ""Â2. Generalized Calderónâ€?Zygmund Operators""; ""2.1 Some preliminary background and motivation""; ""2.2 Generalized Calderónâ€?Zygmund operators and functions of polynomial growth""; ""2.3 The Weak Boundedness Property""; ""Â3. Generalized Calderónâ€?Zygmund Operators on Triebelâ€?Lizorkin Spaces""
- ""References""
- Notes:
- "March 1991, Volume 90, Number 442 (second of 3 numbers)."
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 1-4704-0868-6
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