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

By: Lars I. Hedberg (author), Yuri Netrusov (author)Paperback

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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.

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.

Product Details

• ISBN13: 9780821839836
• Format: Paperback
• Number Of Pages: 97
• ID: 9780821839836
• ISBN10: 0821839837

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