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

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Müller D., Prestini E.

Colloquium Mathematicum

2010

tom 118

nr 1

333-347

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 $log(2+L_{α})f ∈ L²$, 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 → ∞.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Müller D.

1 Prestini E.

1 2010

Wyniki wyszukiwania

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