This article is cited 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.

UDC: 517.982

MSC: Primary 46B70; Secondary 46M35

Received: 12.11.2012 and 28.10.2013

DOI: 10.4213/sm8192

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

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