69 citations · 257 across the 37 of their papers we have counts for
17 papers · 1 filter
Polynomial sequences in discrete nilpotent groups of step 2
Alexandru D. Ionescu, Akos Magyar, Mariusz Mirek +1
We discuss some of our work on averages along polynomial sequences in nilpotent groups of step 2. Our main results include boundedness of associated maximal functions and singular…
Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions
Adam Nowak, Luz Roncal, Tomasz Z. Szarek
We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions $M^{\a,\b}_t$ to be bounded on power weighted Lebes…
Dimension-free estimates for the discrete spherical maximal functions
Mariusz Mirek, Tomasz Z. Szarek, Błażej Wróbel
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein and Wainger) corresponding to the Euclidean spheres in with dyadic radii have $…
Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex
Adam Nowak, Peter Sjögren, Tomasz Z. Szarek
We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors' recent result obtained for a Euclidean…
Analysis in the multi-dimensional ball
Peter Sjögren, Tomasz Z. Szarek
We study the heat semigroup maximal operator associated with a well-known orthonormal system in the d-dimensional ball. The corresponding heat kernel is shown to satisfy Gaussian b…
Sharp estimates of the spherical heat kernel
Adam Nowak, Peter Sjögren, Tomasz Z. Szarek
We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.
Lusin area integrals related to Jacobi expansions
Tomasz Z. Szarek
We investigate mixed Lusin area integrals associated with Jacobi trigonometric polynomial expansions. We prove that these operators can be viewed as vector-valued Calderón-Zygmund…
Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions
Adam Nowak, Peter Sjögren, Tomasz Z. Szarek
Classical settings of discrete and continuous orthogonal expansions, like Laguerre, Bessel and Jacobi, are associated with second order differential operators playing the role of t…
On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
Adam Nowak, Krzysztof Stempak, Tomasz Z. Szarek
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to $\m…
Riesz-Jacobi transforms as principal value integrals
Alejandro J. Castro, Adam Nowak, Tomasz Z. Szarek
We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz-Jacobi transforms of odd orders expr…
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
Alejandro J. Castro, Tomasz Z. Szarek
We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to (als…
Analysis related to all admissible type parameters in the Jacobi setting
Adam Nowak, Peter Sjögren, Tomasz Z. Szarek
We derive an integral representation for the Jacobi-Poisson kernel valid for all admissible type parameters in the context of Jacobi expansions. This enables us to develop a…
Calderón-Zygmund operators in the Bessel setting for all possible type indices
Alejandro J. Castro, Tomasz Z. Szarek
In this paper we adapt the technique developed in [17] to show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type…
Calderón-Zygmund operators related to Laguerre function expansions of convolution type
Adam Nowak, Tomasz Szarek
We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices in th…
Multipliers of Laplace transform type in certain Dunkl and Laguerre settings
Tomasz Szarek
We investigate Laplace type and Laplace-Stieltjes type multipliers in the -dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorph…
On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings
Tomasz Szarek
We investigate -functions and Lusin's area type integrals related to certain multi-dimensional Dunkl and Laguerre settings. We prove that the considered square functions are bou…
Littlewood-Paley-Stein type square functions based on Laguerre semigroups
Tomasz Szarek
We investigate g-functions based on semigroups related to multi-dimensional Laguerre function expansions of convolution type. We prove that these operators can be viewed as Caldero…