2-WEIGHTED ESTIMATES FOR INTEGRAL-OPERATO RS

Conditions on the nonnegative weight functions u(x) and v(x) which ens ure that an integral operator [GRAPHICS] x is-an-element-of Q subset-o f R(n), n greater-than-or-equal-to 1, maps the space L(p) (u; OMEGA) = = {f : \\uf\\p < infinity}, 0 < p less-than-or-equal-to infinity, int o the space L(q) (v; OMEGA), 0 < q less-than-or-equal-to infinity. In particular, two weight estimates for one-dimensional integral operator s with the kernel K(x, t)=0 for x<t and for multidimensional operators of potential type are considered. The discrete analogue of the result s being obtained are stated.