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Mat. Sb., 2014, Volume 205, Number 1, Pages 87–104 (Mi msb8192)  

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

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


DOI: https://doi.org/10.4213/sm8192

Full text: PDF file (552 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:1, 83–100

Bibliographic databases:

UDC: 517.982
MSC: Primary 46B70; Secondary 46M35
Received: 12.11.2012 and 28.10.2013

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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  • http://mi.mathnet.ru/eng/msb/v205/i1/p87

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Ovchinnikov, “Interpolation functions and the Lions–Peetre interpolation construction”, Russian Math. Surveys, 69:4 (2014), 681–741  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. L. Kussainova, A. Ospanova, “Interpolation Theorems For Weighted Sobolev Spaces”, World Congress on Engineering, WCE 2015, Vol I, Lecture Notes in Engineering and Computer Science, ed. Ao S. Gelman L. Hukins D. Hunter A. Korsunsky A., Int. Assoc. Engineers-Iaeng, 2015, 25–28  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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