Hausdorff operators and fractional Hausdorff operators in the Dunkl setting

2026/06/15 by Sumit Parashar, Saswata Adhikari
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Abstract

In this paper, we investigate the boundedness properties of the Dunkl-type Hausdorff operator on Dunkl-type Morrey spaces and Dunkl-type Campanato spaces. Furthermore, we introduce the fractional Dunkl-type Hausdorff operator and study its boundedness from L^p(ℝ, dμ_α) to L^q(ℝ, dμ_α). We also establish the boundedness of the fractional Dunkl-type Hausdorff operator on Dunkl-type Morrey spaces under suitable conditions.

Citations

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

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