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

2026/07/24 by Jian Tan
#math.CA #math.FA

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Abstract

In this paper, we identify the dual spaces of variable Dunkl--Hardy spaces using a discrete Dunkl--Calderón reproducing formula and the Frazier and Jawerth's method adapted to the variable exponent setting. Furthermore, we prove a T1 theorem for Dunkl--Calderón--Zygmund operators acting on variable Dunkl--Hardy spaces and on their dual spaces via using almost orthogonal estimate, the duality result and the density argument.

Citations

• Variable Hardy spaces in the Dunkl Setting
• Hardy spaces with variable exponents and generalized Campanato spaces
• Convolution operator and maximal function for the Dunkl transform
• Hp spaces of several variables
• Differential-difference operators associated to reflection groups

Related

• Variable Hardy spaces in the Dunkl Setting
• Variable Hardy Spaces
• Some results on the Hardy space H1 associated with the Dunkl operators
• Singular integral operators, T1 theorem, Littlewood-Paley theory and Hardy spaces in Dunkl Setting
• Maximal operator in Dunkl-Fofana spaces