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Sbornik: Mathematics, 2014, Volume 205, Issue 1, Pages 83–100
DOI: https://doi.org/10.1070/SM2014v205n01ABEH004368 (Mi sm8192) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces

V. I. Ovchinnikov

Voronezh State University
English version PDF (511 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2014v205n01ABEH004368
Abstract: In the paper, a new description of the generalized Lions-Peetre method of means is found, which enables one to evaluate the interpolation orbits of spaces constructed by this method. The list of these spaces includes all Lorentz spaces with functional parameters, Orlicz spaces, and spaces close to them. This leads in turn to new optimal embedding theorems for Sobolev spaces produced using the Lions-Peetre construction in rearrangement invariant spaces. It turns out that the optimal space of the embedding is also a generalized Lions-Peetre space whose parameters are explicitly evaluated.
Bibliography: 18 titles.
Keywords: embedding theorems, Sobolev spaces, rearrangement invariant spaces, interpolation orbits, generalized Lions-Peetre spaces of means.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00378
Received: 12.11.2012 and 28.10.2013
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 1, Pages 87–104
DOI: https://doi.org/10.4213/sm8192
Bibliographic databases:
Document Type: Article
UDC: 517.982
MSC: Primary 46B70; Secondary 46M35
Language: English
Original paper language: Russian
Citation: V. I. Ovchinnikov, “Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces”, Mat. Sb., 205:1 (2014), 87–104; Sb. Math., 205:1 (2014), 83–100
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v205/i1/p87
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:457
    Russian version PDF:202
    English version PDF:14
    References:72
    First page:39
     
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