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

• Autorzy: D. Müller , E. Prestini
• Języki publikacji: EN

Abstrakty

EN

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 → ∞.

Kategorie tematyczne

• 43A50: Convergence of Fourier series and of inverse transforms
• 22E30: Analysis on real and complex Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 1
• Strony: 333-347

Daty

wydano

2010

Twórcy

autor

D. Müller

• Mathematisches Seminar, C.A.-Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany

autor

E. Prestini

• Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

Identyfikatory

DOI

10.4064/cm118-1-18