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$%B. Vedel, Besov characteristic of a distribution, Rev. Mat. Complut. 20 (2007), no. 2, 407–421.%$

Besov Characteristic of a Distribution
Béatrice VEDEL
Laboratoire d’Analyse et de Mathématiques Appliqués
Université Paris XII
Avenue du Général De Gaulle
94010 Créteil Cedex — France
beatrice.vedel@u-picardie.fr

Received: December 23, 2006
Accepted: March 5, 2007

ABSTRACT

The Besov characteristic of a distribution f is the function sf defined for 0 ≤ t < ∞ by

sf(t)= sup{ s∈ ℝ; f ∈ Bs1∕t,1(ℝn)}.

We give in this paper a criterion for a function Γ defined on [0, +∞[ to be the Besov characteristic of a distribution. Generalizations of this criterion to particular weighted Besov spaces and to anisotropic Besov spaces are also given.

Key words: Besov spaces, wavelet analysis, weighted Besov spaces, anisotropic Besov spaces, anisotropic wavelet analysis.
2000 Mathematics Subject Classification: 46E35, 42B35, 42C40.