A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces
Baode LiXinjiang University, Urumqi, China
Marcin BownikUniversity of Oregon, Eugene, USA
Dachun YangBeijing Normal University, China
Wen YuanBeijing Normal University, China
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. 125–147DOI 10.4171/ZAA/1503