A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces
Baode Li
Xinjiang University, Urumqi, ChinaMarcin Bownik
University of Oregon, Eugene, USADachun Yang
Beijing Normal University, ChinaWen Yuan
Beijing Normal University, China
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Abstract
In this article, the authors study weighted anisotropic Besov and Triebel-Lizorkin spaces associated with expansive dilations and -weights. The authors show that elements of these spaces are locally integrable when the smoothness parameter is positive. The authors also characterize these spaces for small values of 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].
Cite this article
Baode Li, Marcin Bownik, Dachun Yang, Wen Yuan, A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces. Z. Anal. Anwend. 33 (2014), no. 2, pp. 125–147
DOI 10.4171/ZAA/1503