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

Netrusov, Yuri

Couverture souple

ISBN 10 : 0821839837 ISBN 13 : 9780821839836

Editeur : American Mathematical Society, 2007

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2007
• Langue: anglais
• ISBN 10: 0821839837
• ISBN 13: 9780821839836
• Reliure: Broché
• Nombre de pages: 97
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible