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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 170–187
DOI: https://doi.org/10.4213/tm4137 (Mi tm4137) 		 
On a Limiting Case for Pointwise Multiplication in Nikol'skii–Besov Spaces

Winfried Sickel

Friedrich Schiller University Jena, Ernst-Abbe-Platz 2, 07737 Jena, Germany
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DOI: https://doi.org/10.4213/tm4137
Abstract: We investigate the regularity of the set of all products $f\cdot g$ for $f$ and $g$ belonging to certain Nikol'skii–Besov spaces. The special situation we are interested in has been left open in earlier contributions. It represents a limiting situation. We list a number of positive and negative results, both in the inhomogeneous and in the homogeneous situation.
Keywords: pointwise multipliers, inhomogeneous Nikol'skii–Besov spaces, homogeneous Nikol'skii–Besov spaces, paramultiplication.
Received: March 27, 2020
Revised: August 28, 2020
Accepted: January 20, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 162–178
DOI: https://doi.org/10.1134/S0081543821010090
Bibliographic databases:
Document Type: Article
UDC: 517.518.2
Language: Russian
Citation: Winfried Sickel, “On a Limiting Case for Pointwise Multiplication in Nikol'skii–Besov Spaces”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 170–187; Proc. Steklov Inst. Math., 312 (2021), 162–178
Citation in format AMSBIB
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\paper On a Limiting Case for Pointwise Multiplication in Nikol'skii--Besov Spaces
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 170--187
\publ Steklov Math. Inst.
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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