Weighted multiparameter local Hardy spaces. (English) Zbl 1495.42009

He, Shaoyong; Chen, Jiecheng

Rocky Mt. J. Math. 51, No. 5, 1649-1670 (2021).

Summary: We apply the discrete multiparameter local Calderón identity and Littlewood-Paley-Stein theory with weights to carry out the weighted multiparameter local Hardy spaces \(h_w^p\) of arbitrary \(k\) number of parameters \((k \geq 3)\). We will derive the \((h_w^p, h_w^p)\) and \((h_w^p, L_w^p)\) \((0 < p \leq 1)\) boundedness for multiparameter inhomogeneous singular integral operators with slightly weaker assumptions on the kernel.

MSC:

42B35	Function spaces arising in harmonic analysis
42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25	Maximal functions, Littlewood-Paley theory

Keywords:

weighted multiparameter local Hardy spaces; discrete multiparameter local Calderón identity; multiparameter inhomogeneous singular integral operators; discrete Littlewood-Paley-Stein theory

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