Degree of Convergence of an Integral Operator

TL;DR

This paper investigates the convergence properties of a newly defined integral operator on Lp spaces, providing a unified framework that generalizes many known results and extends to singular integral operators.

Contribution

It introduces a general integral operator on Lp, determines its convergence degree, and derives numerous corollaries including results on singular integral operators.

Findings

Established the degree of convergence of the integral operator.

Unified various known results as special cases.

Extended results to singular integral operators.

Abstract

In this paper we define an integral operator on Lp and obtain its degree of convergence in the appropriate norm. By specializing the kernel of the integral operator we obtain many known results as corollaries. We have also applied our results to obtain results on singular integral operators.