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

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
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