  In this article,we first give a modified Schwarz-Pompeiu formula in a general
sector ring by proper conformal mappings, and obtain the solution of the
Schwarz problem for the Cauchy-Riemann equation in explicit forms. Furthermore,
a class of integral operators is introduced together with their properties.
Finally, by virtue of these operators, Schwarz problems for a inhomogeneous
polyanalytic equation and for a generalized polyanalytic equation are
investigated, respectively.
