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math.CA2026
Remarks on the Ionescu-Wainger multiplier theorem
Dariusz Kosz, Mariusz Mirek, Wojciech SÅomian +1
In this paper, we extend the recent Ionescu--Wainger multiplier theorem for the set of canonical fractions by Kosz, Mirek, Peluse, Wan, and Wright in several directions. First, we…
math.CA2025
Variation of the one-dimensional centered maximal operator on simple functions with gaps between pieces
Paul Hagelstein, Dariusz Kosz, Krzysztof Stempak
Let denote the centered Hardy--Littlewood operator on . We prove that \[ {\rm Var} (Mf)\le {\rm Var} (f) - \frac12\big| |f(\infty)|-|f(-\infty)|\big| \] for piecewi…
math.CA2025
On differentiation of integrals in Lebesgue spaces
Marco Fraccaroli, Dariusz Kosz, Luz Roncal
We study the problem of differentiation of integrals for certain bases in the infinite-dimensional torus . In particular, for every , we construc…