On convergence and divergence of Fourier-Bessel series.
Imaginary powers of the Dunkl harmonic oscillator.
Transplanting Maximal Inequalities Between Laguerre and Hankel Multipliers.
On convolution products of radial measures on the Heisenberg group
Equiconvergence for Laguerre function series
We prove an equiconvergence theorem for Laguerre expansions with partial sums related to partial sums of the (non-modified) Hankel transform. Combined with an equiconvergence theorem recently proved by Colzani, Crespi, Travaglini and Vignati this gives, via the Carleson-Hunt theorem, a.e. convergence results for partial sums of Laguerre function expansions.
Almost everywhere summability of Laguerre series
We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions , n = 0,1,2,..., in , a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function , 1 ≤ p ≤ ∞, converge to f a.e. The main tool we use is a Hardy-Littlewood type maximal operator associated with a generalized Euclidean convolution.
An algebra associated with the generalized sublaplacian
A weighted multiplier theorem for Rockland operators
A note on Zemanian spaces.
On weighted transplantation and multipliers for Laguerre expansions.
Hankel multipliers and transplantation operators
Connections between Hankel transforms of different order for -functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.
Conjugacy for Fourier-Bessel expansions
We define and investigate the conjugate operator for Fourier-Bessel expansions. Weighted norm and weak type (1,1) inequalities are proved for this operator by using a local version of the Calderón-Zygmund theory, with weights in most cases more general than weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed.
Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator
We propose a definition of Riesz transforms associated to the Ornstein-Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding spaces, 1 < p < ∞.
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