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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 98–110
DOI: https://doi.org/10.4213/tm4127 (Mi tm4127) 		 
Interpolation of Spaces of Functions of Positive Smoothness on a Domain

O. V. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
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DOI: https://doi.org/10.4213/tm4127
Abstract: Interpolation spaces are described for spaces of functions of positive smoothness on a domain $G$ of the Euclidean space $\mathbb R^n$ that satisfies the flexible cone condition. As a consequence, multiplicative estimates for the norms of functions are obtained. The arguments are based on integral representations of functions over a flexible cone in terms of the local approximations of functions by polynomials and on estimates of the arising convolution operators.
Keywords: regular domain, spaces of functions of positive smoothness, interpolation, multiplicative estimates.
Received: May 22, 2020
Revised: September 5, 2020
Accepted: November 17, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 91–103
DOI: https://doi.org/10.1134/S0081543821010053
Bibliographic databases:
Document Type: Article
UDC: 517.518.2
Language: Russian
Citation: O. V. Besov, “Interpolation of Spaces of Functions of Positive Smoothness on a Domain”, 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, 98–110; Proc. Steklov Inst. Math., 312 (2021), 91–103
Citation in format AMSBIB
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\paper Interpolation of Spaces of Functions of Positive Smoothness on a Domain
\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 98--110
\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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