Discrete singular integrals in a half-space

Abstract

We consider Calderon-Zygmund singular integral in the discrete halfspace hZm+, where Zm is entire lattice (h > 0) in Rm, and prove, that the discrete singular integral operator is invertible in L2(hZm+) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.