Pointwise convergence analysis for nonlinear double m-singular integral operators

Abstract

In this chapter, m-singularity notion is discussed for double singular integral operators. In this direction, several results concerning pointwise convergence of nonlinear double m-singular integral operators are presented. This chapter is divided into six sections. In the first section, the reasons giving birth to m-singularity notion are explained and related theoretical background is mentioned. Also, the motivations giving inspiration to this note are presented. In the second section, the well-definiteness of the operators which are under the spotlights is shown on their domain. In the third section, an auxiliary result, pointwise convergence theorem, is proved. In the fourth section, main theorem, Fatou type convergence theorem, is proved. In the fifth section, corresponding rates of convergences are evaluated. In the last section, some concluding remarks are given.