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

D. Müller; E. Prestini

D. Müller ; E. Prestini

Colloquium Mathematicae, Tome 120 (2010), p. 333-347 / Harvested from The Polish Digital Mathematics Library

Résumé

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 → ∞.

Publié le : 2010-01-01

Zbl 1205.22008

EUDML-ID : urn:eudml:doc:283574

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     author = {D. M\"uller and E. Prestini},
     title = {A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups},
     journal = {Colloquium Mathematicae},
     volume = {120},
     year = {2010},
     pages = {333-347},
     zbl = {1205.22008},
     language = {en},
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D. Müller; E. Prestini. A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups. Colloquium Mathematicae, Tome 120 (2010) pp. 333-347. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-1-18/