Characterizations of weighted Triebel–Lizorkin spaces with variable smoothness and integrability

Authors

  • Shengrong Wang School of Mathematics and Statistics, Hainan Normal University, Haikou, China
  • Pengfei Guo School of Mathematics and Statistics, Hainan Normal University, Haikou, China
  • Jingshi Xu School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China; Center for Applied Mathematics of Guangxi (GUET), Guilin, China; Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin, China

DOI:

https://doi.org/10.3842/umzh.v78i9-10.9636

Keywords:

Triebel-Lizorkin, Muckenhoupt weight, variable exponent, Peetre's maximal function, Lusin area function, $g^\ast_\lambda$-function, atom, molecule, wavelet.

Abstract

UDC 517.98; 517.51

We first establish the characterizations of weighted Triebel–Lizorkin spaces with variable exponents via the Peetre's maximal functions,  the Lusin area function, and the Littlewood–Paley $g^\ast_\lambda$-function. Then we obtain the decomposition characterizations of these spaces by atoms, molecules, and wavelets. Finally, as an application, we prove the boundedness of pseudo-differential operators on these spaces.

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 78, No. 9-10, 2026.

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Published

19.09.2026

Issue

Vol. 78 No. 9-10 (2026)

Section

Research articles