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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Summary: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
Bibliography:Includes bibliographical references (p. 253-255)
July 2023, volume 287, number 1426 (fourth of 6 numbers)
ISBN:9781470459901
1470459906
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1426