Discrete Singular Integrals in a Half-Space

Part of the Trends in Mathematics book series (TM)

Abstract

We consider Calderon–Zygmund singular integral in the discrete half-space \(h\mathbf{Z}^{m}_{+}\), where Zm is entire lattice (h>0) in Rm, 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.

Keywords

Calderon–Zygmund kernel Discrete singular integral Symbol 

Mathematics Subject Classification (2010)

42A50 42A85 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematical AnalysisBelgorod State UniversityBelgorodRussia
  2. 2.Chair of Pure MathematicsLipetsk State Technical UniversityLipetskRussia

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