AE CONVERGENCE OF ANISOTROPIC PARTIAL FOURIER INTEGRALS ON EUCLIDEAN SPACES AND HEISENBERG GROUPS

作者：Mueller D^*; Prestini E

来源：Colloquium Mathematicum, 2010, 118(1): 333-347.

DOI：10.4064/cm118-1-18

• Rademacher-Men'shov theorem
• Heisenberg group
• sub-Laplacian
• spectral integral

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 L(2)-function f lies in the logarithmic Sobolev space given by log(2 + L(alpha)) f is an element of L(2), where L(alpha) 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 -> infinity.

• 出版日期2010