Until now, no book has systematically presented the recently
developed concept of envelopes in function spaces. Envelopes are
relatively simple tools for the study of classical and more
complicated spaces, such as Besov and Triebel-Lizorkin types, in
limiting situations. This theory originates from the classical
result of the Sobolev embedding theorem, ubiquitous in all areas of
functional analysis.
Self-contained and accessible, Envelopes and Sharp Embeddings of
Function Spaces provides the first detailed account of the new
theory of growth and continuity envelopes in function spaces. The
book is well structured into two parts, first providing a
comprehensive introduction and then examining more advanced topics.
Some of the classical function spaces discussed in the first part
include Lebesgue, Lorentz, Lipschitz, and Sobolev. The author
defines growth and continuity envelopes and examines their
properties. In Part II, the book explores the results for function
spaces of Besov and Triebel-Lizorkin types. The author then
presents several applications of the results, including Hardy-type
inequalities, asymptotic estimates for entropy, and approximation
numbers of compact embeddings.
As one of the key researchers in this progressing field, the
author offers a coherent presentation of the recent developments in
function spaces, providing valuable information for graduate
students and researchers in functional analysis.
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