Search Results - "Szarek, Tomasz Z."

Polynomial sequences in discrete nilpotent groups of step 2 by Ionescu, Alexandru D., Magyar, Ákos, Mirek, Mariusz, Szarek, Tomasz Z.

“…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…”
Get full text

Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives by Mirek, Mariusz, Szarek, Tomasz Z, Wright, James

“…In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will…”
Get full text

Polynomial averages and pointwise ergodic theorems on nilpotent groups by Ionescu, Alexandru D., Magyar, Ákos, Mirek, Mariusz, Szarek, Tomasz Z.

“…We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving…”
Get full text

Dimension-Free Estimates for the Discrete Spherical Maximal Functions by Mirek, Mariusz, Szarek, Tomasz Z, Wróbel, Błażej

“…Abstract We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein, and Wainger) corresponding to the Euclidean spheres in…”
Get full text

Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres by Iosevich, Alex, Langowski, Bartosz, Mirek, Mariusz, Szarek, Tomasz Z.

“…We establish an asymptotic formula for the number of lattice points in the sets S h 1 , h 2 , h 3 ( λ ) : = x ∈ Z + 3 : ⌊ h 1 ( x 1 ) ⌋ + ⌊ h 2 ( x 2 ) ⌋ + ⌊ h…”
Get full text

Lusin area integrals related to Jacobi expansions by Szarek, Tomasz Z.

“…We investigate mixed Lusin area integrals associated with Jacobi trigonometric polynomial expansions. We prove that these operators can be viewed as…”
Get full text

Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex by Nowak, Adam, Sjögren, Peter, Szarek, Tomasz Z.

“…We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors’ recent result…”
Get full text

On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings by Nowak, Adam, Stempak, Krzysztof, Szarek, Tomasz Z.

“…We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of…”
Get full text

Riesz–Jacobi Transforms as Principal Value Integrals by Castro, Alejandro J., Nowak, Adam, Szarek, Tomasz Z.

“…We establish an integral representation for the Riesz transforms naturally associated with classical Jacobi expansions. We prove that the Riesz–Jacobi…”
Get full text

Calderón-Zygmund operators in the Bessel setting for all possible type indices by Castro, Alejandro J., Szarek, Tomasz Z.

“…We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of…”
Get full text

Maximal operators of exotic and non-exotic Laguerre and other semigroups associated with classical orthogonal expansions by Nowak, Adam, Sjögren, Peter, Szarek, Tomasz Z.

“…Classical settings of discrete and continuous orthogonal expansions, like those of Laguerre, Bessel and Jacobi, are associated with second order differential…”
Get full text

Calderón–Zygmund operators related to Laguerre function expansions of convolution type by Nowak, Adam, Szarek, Tomasz Z.

“…We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type…”
Get full text

On fundamental harmonic analysis operators in certain Dunkl and Bessel settings by Castro, Alejandro J., Szarek, Tomasz Z.

“…We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to…”
Get full text

ANALYSIS IN THE MULTI-DIMENSIONAL BALL by Sjögren, Peter, Szarek, Tomasz Z.

“…We study the heat semigroup maximal operator associated with a well-known orthonormal system in the $d$ -dimensional ball. The corresponding heat kernel is…”
Get full text

On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings by Szarek, Tomasz Z.

“…We investigate $g$‐functions and Lusin's area type integrals related to certain multi‐dimensional Dunkl and Laguerre settings. We prove that the considered…”
Get full text

Analysis Related to All Admissible Type Parameters in the Jacobi Setting by Nowak, Adam, Sjögren, Peter, Szarek, Tomasz Z.

“…We derive an integral representation for the Jacobi–Poisson kernel valid for all admissible type parameters α , β in the context of Jacobi expansions. This…”
Get full text

CalderSn-Zygmund Operators in the Bessel Setting for All Possible Type Indices by Alejandro J. CASTRO Tomasz Z. SZAREK

“…We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of…”
Get full text

New sharp bounds for the Jacobi heat kernel via an extension of the Dijksma-Koornwinder formula by Nowak, Adam, Sjögren, Peter, Szarek, Tomasz Z

“…We obtain sharp estimates for the Jacobi heat kernel in a range of parameters where the result has not been established before. This extends and completes an…”
Get full text

Endpoint estimates and optimality for the generalized spherical maximal operator on radial functions by Nowak, Adam, Roncal, Luz, Szarek, Tomasz Z

“…Commun. Pure Appl. Anal. 22 (2023), 2233-2277 We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on…”
Get full text

Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives by Mirek, Mariusz, Szarek, Tomasz Z, Wright, James

“…In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will…”
Get full text