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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 269, Pages 91–111 (Mi tm2889)  
This article is cited in 29 scientific papers (total in 29 papers)

Optimal embeddings of generalized Bessel and Riesz potentials

M. L. Goldman

Peoples' Friendship University of Russia, Moscow, Russia
Full-text PDF (262 kB) Citations (29)
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Abstract: We study a space of potentials on the $n$-dimensional Euclidean space that are constructed on the basis of rearrangement-invariant spaces (RISs) by means of convolutions with kernels of general form. These spaces include the classical spaces of Bessel and Riesz potentials as particular cases. We examine the integral properties of the potentials and find necessary and sufficient conditions for their embedding in an RIS. Optimal RISs for such embeddings are also described.
Received in November 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 269, Pages 85–105
DOI: https://doi.org/10.1134/S0081543810020082
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: M. L. Goldman, “Optimal embeddings of generalized Bessel and Riesz potentials”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Trudy Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 91–111; Proc. Steklov Inst. Math., 269 (2010), 85–105
Citation in format AMSBIB
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\paper Optimal embeddings of generalized Bessel and Riesz potentials
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
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\vol 269
\pages 91--111
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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