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Some estimates for \(p\)-adic fractional integral operator and its commutators on \(p\)-adic Herz spaces with rough kernels

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Abstract

In this note we study the boundedness of \(p\)-adic fractional integral operator with rough kernels on \(p\)-adic Herz spaces. Moreover, we establish Lipschitz estimates for commutators of \(p\)-adic fractional integral operator with rough kernels on Herz spaces. In addition, we also obtain central bounded mean oscillations\((C{\dot{M}}O)\) estimate for commutators of \(p\)-adic fractional integral operator with rough kernels on \(p\)-adic Herz spaces. As an application, we characterize \(p\)-adic Herz space in terms of wavelets in continuously differentiable functions \(({\mathcal {C}}^{1}({\mathbb {Q}}_p^n))\) with compact support.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia for funding this work through research groups program under grant number R.G. P-1/129/43.

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Authors and Affiliations

  1. Department of Mathematics, University of Kotli Azad Jammu and Kashmir, Kotli, Pakistan

    Naqash Sarfraz

  2. Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

    Muhammad Aslam

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  1. Naqash Sarfraz
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Correspondence to Naqash Sarfraz.

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Sarfraz, N., Aslam, M. Some estimates for \(p\)-adic fractional integral operator and its commutators on \(p\)-adic Herz spaces with rough kernels. Fract Calc Appl Anal 25, 1734–1755 (2022). https://doi.org/10.1007/s13540-022-00064-w

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  • DOI: https://doi.org/10.1007/s13540-022-00064-w

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