Embeddings of Decomposition Spaces

Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A decomposition space We establish readily verifiable criteria which ensure the existence of a continuous inclusion (“an embedding”) In a nutshell...

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Hlavní autor: Voigtlaender, Felix
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2023
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Decomposition (Mathematics)
Functional analysis-Research
embeddings
Coorbit spaces
Function spaces
<inline-formula content-type="math/mathml"> α \alpha </inline-formula>-modulation spaces
smoothness spaces
decomposition spaces
frequency coverings
Besov spaces
ISBN:9781470459901, 1470459906
ISSN:0065-9266, 1947-6221
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Abstract Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A decomposition space We establish readily verifiable criteria which ensure the existence of a continuous inclusion (“an embedding”) In a nutshell, in order to apply the embedding results presented in this article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings. These sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of We also prove a The resulting embedding theory is illustrated by applications to
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Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A decomposition space We establish readily verifiable criteria which ensure the existence of a continuous inclusion (“an embedding”) In a nutshell, in order to apply the embedding results presented in this article, no knowledge of Fourier analysis is required; instead, one only has to study the geometric properties of the involved coverings, so that one can decide the finiteness of certain sequence space norms defined in terms of the coverings. These sufficient criteria are quite sharp: For almost arbitrary coverings and certain ranges of We also prove a The resulting embedding theory is illustrated by applications to
Author Voigtlaender, Felix
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Keywords embeddings
Coorbit spaces
Function spaces
<inline-formula content-type="math/mathml"> α \alpha </inline-formula>-modulation spaces
smoothness spaces
decomposition spaces
frequency coverings
Besov spaces
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Notes Includes bibliographical references (p. 253-255)
July 2023, volume 287, number 1426 (fourth of 6 numbers)
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Snippet Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two such spaces, is there an embedding between the two? A...
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SubjectTerms Decomposition (Mathematics)
Functional analysis-Research
TableOfContents Introduction -- Different classes of coverings and their relations -- (Fourier-side) decomposition spaces -- Nested sequence spaces -- Sufficient conditions for embeddings -- Necessary conditions for embeddings -- An overview of the derived embedding results -- Decomposition spaces as spaces of tempered distributions -- Applications
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Motivation and related work -- 1.2. Notation -- A comment on the writing style and the length of the paper -- 1.3. Overview of new results -- 1.4. Structure of the paper -- Acknowledgments -- Chapter 2. Different classes of coverings and their relations -- 2.1. Admissible and (semi/almost)-structured coverings -- 2.2. Relations between coverings -- Chapter 3. (Fourier-side) decomposition spaces -- 3.1. Convolution relations for ^{ }, ∈(0,1) -- 3.2. Definition of decomposition spaces -- 3.3. Well-definedness of decomposition spaces -- 3.4. Completeness of decomposition spaces -- Chapter 4. Nested sequence spaces -- Chapter 5. Sufficient conditions for embeddings -- Chapter 6. Necessary conditions for embeddings -- 6.1. Elementary necessary conditions -- 6.2. Coincidence of decomposition spaces -- 6.3. Improved necessary conditions -- 6.4. Further necessary conditions in case of ₁= ₂ -- 6.5. Complete characterizations for relatively moderate coverings -- Chapter 7. An overview of the derived embedding results -- 7.1. A collection of readily applicable embedding results -- 7.2. Embeddings between decomposition spaces: A user's guide -- Chapter 8. Decomposition spaces as spaces of tempered distributions -- Chapter 9. Applications -- 9.1. Embeddings of -modulation spaces -- 9.2. Embeddings between -modulation spaces and Besov spaces -- 9.3. Embeddings between homogeneous and inhomogeneous Besov spaces -- Bibliography -- Back Cover
Title Embeddings of Decomposition Spaces
URI https://www.ams.org/memo/1426/
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