1 citations · 1 across the 9 of their papers we have counts for
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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 construct…
On the doubling condition in the infinite-dimensional setting
Dariusz Kosz
We present a systematic approach to the problem whether a topologically infinite-dimensional space can be made homogeneous in the Coifman--Weiss sense. The answer to the examined q…
The maximal function of the Devil's staircase is absolutely continuous
Cristian González-Riquelme, Dariusz Kosz
We study the problem of whether the centered Hardy--Littlewood maximal function of a singular function is absolutely continuous. For a parameter and a closed set $E\s…
Maximal operators in nondoubling metric measure spaces
Dariusz Kosz
This is a revised version of the doctoral dissertation of the same title, written under the supervision of Professor Krzysztof Stempak in 2019. For general (possibly nondoubling) m…
Maximal operators on the infinite-dimensional torus
Dariusz Kosz, Javier Martínez Perales, Victoria Paternostro +2
We study maximal operators related to bases on the infinite-dimensional torus . {For the normalized Haar measure on it is known that $M^{\mathcal{…
condition for general bases revisited: complete classification of definitions
Dariusz Kosz
We refer to the discussion on different characterizations of the class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi. Twelve definitions of the $A_\…