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Convolution operators and Bochner-Riesz means on Herz-type Hardy spaces in the Dunkl setting. (English) Zbl 1213.44003

For T𝒮 ' () and f𝒮(), the Dunkl convolution product T* α f is defined by

T* α f(x)=T(y),τ x f(-y),x,

where τ x is the Dunkl translation operator. The author investigates the Dunkl convolution operators on Herz-type Hardy spaces α,2 p and establishes a version of multiplier theorem for the maximal Bochner-Riesz operators on the Herz-type Hardy spaces α, p . Some related results are contained in the paper by S. Lu and D. Yang [Proc. Am. Math. Soc. 126, No. 11, 3337–3346 (1998; Zbl 0905.42007)].

44A35Convolution (integral transforms)
42B15Multipliers, several variables