JournalszaaVol. 33, No. 2pp. 125–147

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

  • Baode Li

    Xinjiang University, Urumqi, China
  • Marcin Bownik

    University of Oregon, Eugene, USA
  • Dachun Yang

    Beijing Normal University, China
  • Wen Yuan

    Beijing Normal University, China
A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces cover
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Abstract

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

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