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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Bibliographic Details
Main Author: Voigtlaender, Felix
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
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
Online Access:Get full text
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Table of Contents:
  • 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