For one class of the singular integro-differential equations with Cauchy kernel on an interval, a Galerkin method is justified. The convergence is proved and the error estimation is given.

Let X be a non-singular projective complex surface. We can show that Bloch's conjecture (i.e. , that if p g = 0 then the Albanese kernel vanishes) is equivalent to the following statement:

Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...

In this note the authors prove the Lp(Rn×Rm)-boundedness for a class of maximal singular integral operators with rough kernel on product spaces. This extends a result obtained by Chen and Wang in 1992.

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nyström method is applied to the regularized equation. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The spe...