Two Types of Rubio de Francia Operators on Triebel–Lizorkin and Besov Spaces

We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014 ) and answering Havin’s question to one of the authors. Two versions of Rubio de Francia’s operator are discussed: it is shown that...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2019-06, Vol.25 (3), p.804-818
Main Authors: Malinnikova, Eugenia, Osipov, Nikolay N.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Function space
Interpolation
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Operators
Partial Differential Equations
Signal,Image and Speech Processing
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Summary:We discuss generalizations of Rubio de Francia’s inequality for Triebel–Lizorkin and Besov spaces, continuing the research from Osipov (Sb Math 205(7): 1004–1023, 2014 ) and answering Havin’s question to one of the authors. Two versions of Rubio de Francia’s operator are discussed: it is shown that exponential factors are needed for the boundedness of the operator in some smooth spaces while they are not essential in other spaces. We study the operators on some “end” spaces of the Triebel–Lizorkin scale and then use usual interpolation methods.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-018-9617-3