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1
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Equiconvergence for Laguerre function series

100%
Stempak K.
Studia Mathematica
|
1996
|
tom 118
|
nr 3
285-300
EN
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.
2
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Almost everywhere summability of Laguerre series

100%
Stempak K.
Studia Mathematica
|
1991
|
tom 100
|
nr 2
129-147
EN
We apply a construction of generalized twisted convolution to investigate almost everywhere summability of expansions with respect to the orthonormal system of functions $ℓ_n^a(x) = (n!/Γ(n+a+1))^{1/2} e^{-x/2} L_n^a(x)$, n = 0,1,2,..., in $L^2(ℝ_+, x^adx)$, a ≥ 0. We prove that the Cesàro means of order δ > a + 2/3 of any function $f ∈ L^p(x^adx)$, 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.
3
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Hankel multipliers and transplantation operators

64%
Stempak K., Trebels W.
Studia Mathematica
|
1997
|
tom 126
|
nr 1
51-66
EN
Connections between Hankel transforms of different order for $L^p$-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.
4
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Conjugacy for Fourier-Bessel expansions

64%
Ciaurri Ó., Stempak K.
Studia Mathematica
|
2006
|
tom 176
|
nr 3
215-247
EN
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 $A_{p}$ weights. Also results on Poisson and conjugate Poisson integrals are furnished for the expansions considered. Finally, an alternative conjugate operator is discussed.
5
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Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

51%
Nowak A., Roncal L., Stempak K.
Colloquium Mathematicum
|
2010
|
tom 118
|
nr 2
669-684
EN
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 $L^{p}$ spaces, 1 < p < ∞.
6
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On convolution products of radial measures on the Heisenberg group

50%
Stempak K.
Colloquium Mathematicum
|
1985-1986
|
tom 50
|
nr 1
125-128
7
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A weighted multiplier theorem for Rockland operators

44%
Stempak K.
Colloquium Mathematicum
|
1987
|
tom 51
|
nr 1
335-344
8
Content available remote

An algebra associated with the generalized sublaplacian

38%
Stempak K.
Studia Mathematica
|
1988
|
tom 88
|
nr 3
245-256
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