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Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 38–55 (Mi tm3534)  

Correction theorem for Sobolev spaces constructed by a symmetric space

E. I. Berezhnoi

Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: A sharp correction theorem is established for Sobolev spaces in which the norm (quasinorm) of generalized derivatives is calculated in an arbitrary symmetric space. The exact relation between the norm of a corrected function in the Lipschitz space and the measure of the set on which the corrected and original functions are different makes it possible to characterize the Sobolev spaces constructed on the basis of the Marcinkiewicz space in terms of correctability. This opens a way to constructing Sobolev–Marcinkiewicz spaces for functions with an arbitrary domain of definition.

DOI: https://doi.org/10.1134/S0371968514010038

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 32–49

Bibliographic databases:

Document Type: Article
UDC: 517.518.23
Received in March 2013

Citation: E. I. Berezhnoi, “Correction theorem for Sobolev spaces constructed by a symmetric space”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 38–55; Proc. Steklov Inst. Math., 284 (2014), 32–49

Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
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\vol 284
\pages 38--55
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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