Pointwise multipliers on inhomogeneous Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type. (English) Zbl 1271.46031

Han, Yanchang

Taiwanese J. Math. 17, No. 1, 179-206 (2013).

Summary: Using the discrete Calderón reproducing formula of Y.-S. Han et al. [J. Fourier Anal. Appl. 7, No. 6, 571–600 (2001; Zbl 0991.43004)] and the Plancherel-Pólya characterization of the inhomogeneous Besov and Triebel-Lizorkin spaces developed by D.-G. Deng [Commun. Contemp. Math. 6, No. 2, 221–243 (2004; Zbl 1062.43021)], we prove pointwise multipliers on inhomogeneous Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type.

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B25	Maximal functions, Littlewood-Paley theory
42B35	Function spaces arising in harmonic analysis

Keywords:

pointwise multiplier; multiplication operator; Besov and Triebel-Lizorkin space; Calderón reproducing formula; space of homogeneous type

Citations:

Zbl 0991.43004; Zbl 1062.43021