Weak And Strong Boundedness For P-adic Fractional Hausdorff Operator And Its Commutator

TL;DR

This paper studies the boundedness properties of p-adic fractional Hausdorff operators and their commutators across various p-adic function spaces, providing new weak and strong type estimates and conditions.

Contribution

It introduces new boundedness results for p-adic fractional Hausdorff operators and their commutators on multiple p-adic function spaces, including weak Morrey, Lebesgue, and Lorentz spaces.

Findings

Boundedness on weak central Morrey space established

Weak bounds on weighted p-adic weak Lebesgue space derived

Strong type estimates on weighted p-adic Lorentz space obtained

Abstract

In this paper, boundedness of Hausdorff operator on weak central Morrey space is obtained. Furthermore, we investigate the weak bounds of p- adic fractional Hausdorff Operator on weighted p-adic weak Lebesgue Space. We also obtain the sufficient condition of commutators of p-adic fractional Hausdorff Operator by taking symbol function from Lipschitz space. Moreover, strong type estimates for fractional Hausdorff Operator and its commutator on weighted p-adic Lorentz space are also acquired.