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Zeitschrift für Analysis und ihre Anwendungen

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Volume 33, Issue 2, 2014, pp. 125–147
DOI: 10.4171/ZAA/1503

Published online: 2014-04-25

A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces

Baode Li[1], Marcin Bownik[2], Dachun Yang[3] and Wen Yuan[4]

(1) Xinjiang University, Urumqi, China
(2) University of Oregon, Eugene, USA
(3) Beijing Normal University, China
(4) Beijing Normal University, China

In this article, the authors study weighted anisotropic Besov and Triebel-Lizorkin spaces associated with expansive dilations and $A_\infty$-weights. The authors show that elements of these spaces are locally integrable when the smoothness parameter~$\alpha$ is positive. The authors also characterize these spaces for small values of~$\alpha$ 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].

Keywords: Anisotropic expansive dilation, Besov space, Triebel-Lizorkin space, Muckenhoupt weight, square function

Li Baode, Bownik Marcin, Yang Dachun, Yuan Wen: A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces. Z. Anal. Anwend. 33 (2014), 125-147. doi: 10.4171/ZAA/1503