An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation (Memoirs of the American Mathematical Society Vol 188 Issue 882)

LI Hedberg, Y Netrusov

Research output: Book/ReportAuthored book

Abstract

The authors define axiomatically a large class of function (or distribution) spaces on $N$-dimensional Euclidean space. The crucial property postulated is the validity of a vector-valued maximal inequality of Fefferman-Stein type. The scales of Besov spaces ($B$-spaces) and Lizorkin-Triebel spaces ($F$-spaces), and as a consequence also Sobolev spaces, and Bessel potential spaces, are included as special cases. The main results of Chapter 1 characterize our spaces by means of local approximations, higher differences, and atomic representations. In Chapters 2 and 3 these results are applied to prove pointwise differentiability outside exceptional sets of zero capacity, an approximation property known as spectral synthesis, a generalization of Whitney's ideal theorem, and approximation theorems of Luzin (Lusin) type.
Translated title of the contributionAn Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation (Memoirs of the American Mathematical Society Vol 188 Issue 882)
Original languageEnglish
PublisherAmerican Mathematical Society
Number of pages97
ISBN (Print)9780821839836
Publication statusPublished - 2007

Bibliographical note

Other identifier: 0821839837
Other: Series ISSN: 0065-9266

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