Estimates for a Rough Fractional Integral Operator and Its Commutators on p-Adic Central Morrey Spaces

Naqash Sarfraz,Fahd Jarad

doi:10.3390/fractalfract6020117

Abstract

In the current paper, we obtain the boundedness of a rough p-adic fractional integral operator on p-adic central Morrey spaces. Moreover, we establish the λ-central bounded mean oscillations estimate for commutators of a rough p-adic fractional integral operator on p-adic central Morrey spaces.

Highlights

In this day and age, fractional calculus is a key area because of its heaps of applications in engineering science and technology, see for instance [1,2]
Fractional integral operator of order β is defined by fractalfract6020117
The symbol function is from the λ-central bounded mean oscillations(C ṀOs,λ )(Qnp )

Summary

Introduction

In this day and age, fractional calculus is a key area because of its heaps of applications in engineering science and technology, see for instance [1,2]. The fundamental properties of the fractional integral operator on local fields are given in [15]. Λ central bounded mean oscillations estimate for commutators of fractional integral operator on p-adic Morrey spaces are reported in [18]. The boundedness of the fractional integral operator on Morrey spaces is shown in [12,19]. We consider the rough fractional integral operator Tβ,Ω along with its p,b commutator Tβ,Ω and acquire the boundedness on p-adic central Morrey spaces. In the latter case, the symbol function is from the λ-central bounded mean oscillations(C ṀOs,λ )(Qnp ). It is imperative to mention here that our operator is very helpful in finding the regularity of Cauchy problem of Schrödinger equation

Boundedness of Rough p-Adic Fractional Integral Operator on Central

Conclusions