FREDHOLM EQUATION WITH WEIGHTED PARTIAL-INTEGRAL OPERATOR OF POSITIVE ORDER
We study the weighted partial integral operator in Rn in the weighted Lebesgue space LY(D) with the measure of integration hiП=1 xdxj, y2 > -1. The geometric meaning is formally defined and the concept of the order of a weighted partial integral operator is introduced. A sufficient condition for such operators to be bounded in Lp is obtained. The existence and uniqueness of the solution of the weighted Fredholm partial integral equation of the second kind is proved.