Harmonic analysis for a multidimensional discrete Laplacian
Abstract
In this paper we analyze some classical operators in harmonic analysis associated to the multidimensional discrete Laplacian \[ N f(n)=Σi=1N(f(n+ei)-2f(n)+f(n-ei)), n∈ ZN. \] We deal with the heat and Poisson semigroups, the fractional integrals, the Riesz transforms, the fractional powers of the Laplacian, and the gk-square functions.
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