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

D. Müller, and E. Prestini. "A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups." Colloquium Mathematicae 118.1 (2010): 333-347. <http://eudml.org/doc/283574>.

@article{D2010,
abstract = {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 → ∞.},
author = {D. Müller, E. Prestini},
journal = {Colloquium Mathematicae},
keywords = {Rademacher-Men'shov theorem; Heisenberg group; sub-Laplacian; spectral integral},
language = {eng},
number = {1},
pages = {333-347},
title = {A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups},
url = {http://eudml.org/doc/283574},
volume = {118},
year = {2010},
}

TY - JOUR
AU - D. Müller
AU - E. Prestini
TI - A.e. convergence of anisotropic partial Fourier integrals on Euclidean spaces and Heisenberg groups
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 1
SP - 333
EP - 347
AB - 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 → ∞.
LA - eng
KW - Rademacher-Men'shov theorem; Heisenberg group; sub-Laplacian; spectral integral
UR - http://eudml.org/doc/283574
ER -