$$L\log L$$ Type Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space

Abstract

In this paper, the main aim is to prove the weak type \(L \log L\) estimates for commutators of fractional integral operators and the higher order in the context of the p-adic version of Lebesgue spaces, where the symbols of the commutators belong to the p-adic version of \({\text {BMO}}\) space. In addition, we also establish the estimates of the sharp function on the p-adic vector space.