4 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…
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…
Expository article: "Bounded orthogonal systems and the -set problem'' by Jean Bourgain
Hongki Jung, Bartosz Langowski, Alexander Ortiz +1
In this paper, we present an exposition of the work \cite{B} by Jean Bourgain, in which he resolved the well known conjecture posed by Rudin regarding the existence of -sets…