Littlewood–Paley Characterizations of Weighted Anisotropic Triebel–Lizorkin Spaces via Averages on Balls II

  • Jun Liu

    Beijing Normal University, China
  • Dachun Yang

    Beijing Normal University, China
  • Wen Yuan

    Beijing Normal University, China
Littlewood–Paley Characterizations of Weighted Anisotropic Triebel–Lizorkin Spaces via Averages on Balls II cover

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Abstract

This article is the second part of two works of the authors on the same topic. Let be the matrix diag, with , and let be a Muckenhoupt -weight with respect to . In this article, the authors characterize the weighted anisotropic Triebel–Lizorkin space with smoothness order in terms of the Lusin-area function and the Littlewood–Paley -function, defined via the difference between and its ball average

where , denotes the set of all eigenvalues of ,

Further, denotes the step homogeneous quasi-norm associated with and, for any and , . As applications, the authors obtain a series of characterizations for weighted anisotropic Triebel–Lizorkin spaces via pointwise inequalities involving ball averages.

Cite this article

Jun Liu, Dachun Yang, Wen Yuan, Littlewood–Paley Characterizations of Weighted Anisotropic Triebel–Lizorkin Spaces via Averages on Balls II. Z. Anal. Anwend. 39 (2020), no. 1, pp. 1–26

DOI 10.4171/ZAA/1648