A study on convergence of non-convolution type double singular integral operators

The aim of this paper is to investigate the pointwise convergence and the rate of convergence of the operators in the following form: L_{lambda }left( f;x,yright) =underset{Omega }{iint }fleft(t,sright) K_{lambda }left( t,s;x,yright) dsdt, left( x,yright) inOmega, where Omega =times is an arbitrary closed, semi-closed or open region in mathbb{R}^{2}, at a mu-generalized Lebesgue point of fin L_{p}left( Omega right) as left( x,y,lambda right) rightarrow left( x_{0},y_{0},lambda _{0}right) .