Discrete Singular Integrals in a Half-Space

  • Alexander V. Vasilyev
  • Vladimir B. Vasilyev
Part of the Trends in Mathematics book series (TM)


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.


Calderon–Zygmund kernel Discrete singular integral Symbol 

Mathematics Subject Classification (2010)

42A50 42A85 



Many thanks to DAAD and Herr Prof. Dr. Volker Bach for their support.


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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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