Variable Hardy spaces in the Dunkl Setting

2026/07/24 by Jian Tan · 1 citation
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Abstract

In this paper, we aim to define a new variable Hardy spaces in the Dunkl setting by the discrete Littlewood--Paley square functions. We also consider the atomic decomposition characterization for the new variable Hardy spaces with the help of the Littlewood--Paley theory and Hardy spaces on spaces of homogeneous type in the sense of Coifman and Weiss. As applications, we obtain the variable Hardy spaces boundedness for Dunkl--Calderón--Zygmund singular integrals involving by the Euclidean metric and the Dunkl ``metric'' which is associated with the finite reflection groups on the Euclidean space.

Citations

• Convolution operator and maximal function for the Dunkl transform
• Differential-difference operators associated to reflection groups

Cited by

• Dual spaces and T1 theorem of variable Dunkl--Hardy spaces

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