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

Hedberg, Lars Inge; Netrusov, Yuri

Brossura

ISBN 10: 0821839837 ISBN 13: 9780821839836

Casa editrice: Amer Mathematical Society, 2007

Riassunto

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.

Su questo libro

Product Description

Book by Hedberg Lars Inge Netrusov Yuri

Dettagli dell'edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2007
• Lingua: Inglese
• ISBN 10: 0821839837
• ISBN 13: 9780821839836
• Rilegatura: Copertina flessibile
• Numero di pagine: 97
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile