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On Almost Everywhere Convergence.

C. Meaney; E. Prestini — 1993

Monatshefte für Mathematik

A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups

D. Müller; E. Prestini — 2010

Colloquium Mathematicae

We define partial spectral integrals $S_{R}$ on the Heisenberg group by means of localizations to isotropic or anisotropic dilates of suitable star-shaped subsets V containing the joint spectrum of the partial sub-Laplacians and the central derivative. Under the assumption that an L²-function f lies in the logarithmic Sobolev space given by $l o g (2 + L_{α}) f \in L ²$ , where $L_{α}$ is a suitable “generalized” sub-Laplacian associated to the dilation structure, we show that $S_{R} f (x)$ converges a.e. to f(x) as R → ∞.

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