A mean characterization of weighted anisotropic Besov and Triebel-Lizorkin spaces

Abstract

In this article, the authors study weighted anisotropic Besov and Triebel-Lizorkin spaces associated with expansive dilations and A ∞-weights. The authors show that elements of these spaces are locally integrable when the smoothness parameter α is positive. The authors also characterize these spaces for small values of α in terms of a mean square function recently introduced in the context of Sobolev spaces in [Math. Ann. 354 (2012), 589-626] and isotropic Triebel-Lizorkin spaces in [Publ. Mat. 57 (2013), 57-82]. © European Mathematical Society.