skip to main content

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

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.
Authors:
 [1]
  1. Voronezh State University (Russian Federation)
Publication Date:
OSTI Identifier:
22365791
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; INTERPOLATION; MATHEMATICAL SPACE; ORBITS