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+34 946 567 842
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+34 946 567 843
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tzszarek@bcamath.org
Information of interest
Postdoc Fellow at BCAM
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Dimension-Free Estimates for the Discrete Spherical Maximal Functions
Mirek, M.; Szarek, T.Z.
; Wróbel, B. (2024)
We prove that the discrete spherical maximal functions (in the spirit of Magyar, Stein, and Wainger) corresponding to the Euclidean spheres in Zd with dyadic radii have lp(Zd) bounds for all p ∈ [2,∞] independent of the ...
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Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
Iosevich, A.; Langowski, B.; Mirek, M.; Szarek, T.Z. (2023-01-01)
We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ...
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ENDPOINT ESTIMATES AND OPTIMALITY FOR THE GENERALIZED SPHERICAL MAXIMAL OPERATOR ON RADIAL FUNCTIONS
Nowak, A.; Roncal, L.; Szarek, T.Z. (2023)
We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions Mtα,β to be bounded on power weighted Lebesgue spaces. Moreover, we also obtain the corresponding ...
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Polynomial averages and pointwise ergodic theorems on nilpotent groups
Ionescu, A. D.; Magyar, A.; Mirek, M.; Szarek, T.Z. (2022)
We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on $\sigma$-finite measure spaces. We also establish ...
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OSCILLATION INEQUALITIES IN ERGODIC THEORY AND ANALYSIS: ONE-PARAMETER AND MULTI-PARAMETER PERSPECTIVES
Mirek, M.; Szarek, T.Z.; Wright, J. (2022)
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 pay special attention to quantitative aspects of pointwise ...
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Some remarks on oscillation inequalities
Mirek, M.; Wojciech, S.; Szarek, T.Z. (2022)
In this paper, we establish uniform oscillation estimates on Lp(X) with p ∈ (1, ∞) for the polynomial ergodic averages. This result contributes to a certain problem about uniform oscillation bounds for ergodic averages ...