Envelopes and Sharp Embeddings of Function Spaces Research Notes in Mathematics Series

Author	Dorothee D. Haroske
Format	Hardcover
ISBN	9781584887508
Publisher	Chapman And Hall/crc
Manufacturer	Chapman And Hall/crc

This book is about envelopes in function spaces. It provides a comprehensive introduction to the new theory of growth and continuity envelopes in function spaces, and then examines more advanced topics. The book is well structured into two parts, first providing a comprehensive introduction and then examining more advanced topics. Part I covers classical function spaces, while Part II covers Besov and Triebel-Lizorkin type function spaces. The book also explores the results for function spaces of Besov and Triebel-Lizorkin types. Finally, the book presents several applications of the results, including Hardy-type inequalities, asymptotic estimates for entropy, and approximation numbers of compact embeddings.

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.