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

Journal Article · Fri Jan 31 00:00:00 EST 2014 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2014V205N01ABEH004368· OSTI ID:22365791

Ovchinnikov, V I ^[1]

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1. Voronezh State University (Russian Federation)

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.

• OSTI ID: 22365791
• Journal Information: Sbornik. Mathematics, Vol. 205, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CALCULATION METHODS
INTERPOLATION
MATHEMATICAL SPACE
ORBITS