An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation
Author(s)
Bibliographic Information
An axiomatic approach to function spaces, spectral synthesis, and Luzin approximation
（Memoirs of the American Mathematical Society, no. 882）
American Mathematical Society, 2007
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In memoriam Lars Inge Hedberg 1935-2005
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Note
"July 2007, volume 188, number 882 (third of four numbers)"
Bibliography: p. 95-97
Description and Table of Contents
Description
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.
Table of Contents
Introduction. Notation A class of function spaces Differentiability and spectral synthesis Luzin type theorems Appendix. Whitney's approximation theorem in $L_p(\mathbf{R}^N), p>0$ Bibliography.
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