Discrete Singular Integrals in a Half-Space

Abstract

We consider Calderon–Zygmund singular integral in the discrete half-space \(h\mathbf{Z}^{m}_{+}\), where Z m is entire lattice (h>0) in R m , and prove, that the discrete singular integral operator is invertible in \(L_{2}(h\mathbf{Z}^{m}_{+})\) 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.