7 papers
Discrete analogues in harmonic analysis: Multi-parameter Radon averages
Agnieszka Hejna-Åyżwa, Joonil Kim, Bartosz Langowski +3
In this paper we study maximal and oscillation inequalities for multi-parameter discrete Radon averaging operators. We develop a robust variant of the multi-parameter circle method…
Pointwise convergence of polynomial multiple ergodic averages along the primes
Mariusz Mirek, Renhui Wan, James Wright
We establish pointwise almost everywhere convergence for the polynomial multilinear ergodic averages $$\frac{1}{N} \sum_{n=1}^N \La(n) f_1(T^{P_1(n)} x)\cdots f_k(T^{P_k(n)} x)$$ a…
A remark on Kolmogorov's theorem
Arash Lotfi, Mariusz Mirek, Richard K. Yu
The aim of this note is to illustrate that the set of integrable functions on the torus for which the Fourier series diverges almost everywhere is of the second Baire…
Discrete analogues in harmonic analysis: methods
Bartosz Langowski, Mariusz Mirek, Tomasz Z. Szarek
In this note we present how the almost-orthogonality methods based on arguments can be employed to study boundedness of discrete operators of Radon type. Almost-orthogonalit…
Polynomial ergodic theorems in the spirit of Dunford and Zygmund
Dariusz Kosz, Bartosz Langowski, Mariusz Mirek +1
The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on , , for certain multiparameter polynomial ergodic averages in th…
The multilinear circle method and a question of Bergelson
Dariusz Kosz, Mariusz Mirek, Sarah Peluse +2
Let and be a probability space equipped with a family of commuting invertible measure-preserving transformations $T_1,\ldots, T_k \colon…