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arXiv · 2606.16197

Hausdorff operators and fractional Hausdorff operators in the Dunkl setting

Sumit Parashar·Saswata Adhikari
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Abstract

In this paper, we investigate the boundedness properties of the Dunkl-type Hausdorff operator on generalized Dunkl-type Morrey spaces and generalized Dunkl-type Campanato spaces. Furthermore, we introduce the fractional Dunkl-type Hausdorff operator and study its boundedness from $L^p(\mathbb{R}, d\mu_\alpha)$ to $L^q(\mathbb{R}, d\mu_\alpha)$. We also establish the boundedness of the fractional Dunkl-type Hausdorff operator on generalized Dunkl-type Morrey spaces under suitable conditions. As a consequence of our main results, we derive several applications. Finally, we evaluate the exact norm of the Dunkl-type Hausdorff operator on Dunkl-type Morrey spaces and Dunkl-type Campanato spaces.

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Sumit Parashar, Saswata Adhikari. 2026-06-15. Hausdorff operators and fractional Hausdorff operators in the Dunkl setting. https://arxiv.org/abs/2606.16197

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