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1
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Heat-diffusion and Poisson integrals for Laguerre and special Hermite expansions on weighted $L^{p}$ spaces

100%
Nowak A.
Studia Mathematica
|
2003
|
tom 158
|
nr 3
239-268
EN
We investigate heat-diffusion and Poisson integrals associated with Laguerre and special Hermite expansions on weighted $L^{p}$ spaces with $A_{p}$ weights.
2
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Sharp estimates of the Jacobi heat kernel

63%
Nowak A., Sjögren P.
Studia Mathematica
|
2013
|
tom 218
|
nr 3
219-244
EN
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that the maximal operator of the multi-dimensional Jacobi heat semigroup satisfies a weak type (1,1) inequality. We also obtain sharp estimates of the Poisson-Jacobi kernel.
3
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Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

51%
Nowak A., Roncal L., Stempak K.
Colloquium Mathematicum
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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 < ∞.
4
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Mapping properties of fundamental operators in harmonic analysis related to Bessel operators

51%
Betancor J., Harboure E., Nowak A., Viviani B.
Studia Mathematica
|
2010
|
tom 197
|
nr 2
101-140
EN
We obtain sharp power-weighted $L^{p}$, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.
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