**Memoirs of the American Mathematical Society**

2007;
97 pp;
Softcover

MSC: Primary 46;
Secondary 26; 31; 41

Print ISBN: 978-0-8218-3983-6

Product Code: MEMO/188/882

List Price: $66.00

Individual Member Price: $39.60

**Electronic ISBN: 978-1-4704-0486-4
Product Code: MEMO/188/882.E**

List Price: $66.00

Individual Member Price: $39.60

# An Axiomatic Approach to Function Spaces, Spectral Synthesis, and Luzin Approximation

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*Lars Inge Hedberg; Yuri Netrusov*

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.