6 papers · 1 filter
Remarks on the construction of sets associated to trees not satisfying a separation condition
Paul Hagelstein, Blanca Radillo-Murguia, Alex Stokolos
sets involving sticky maps have been used in the theory of differentiation of integrals to probabilistically construct Kakeya-type sets that imply certain types of direct…
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…
Probabilistic Construction of Kakeya-Type Sets in associated to separated sets of directions
Paul Hagelstein, Blanca Radillo-Murguia, Alexander Stokolos
We provide a condition on a set of directions ensuring that the associated directional maximal operator is unbounded on for every…
Sharp Weak Type Estimates for Maximal Operators associated to Rare Bases
Paul Hagelstein, Giorgi Oniani, Alex Stokolos
Let denote a nonempty translation invariant collection of intervals in (which we regard as a rare basis), and define the associated geometric maximal o…
Sharp weak type estimates for a family of Soria bases
Dmitriy Dmitrishin, Paul Hagelstein, Alex Stokolos
Let be a collection of rectangular parallelepipeds in whose sides are parallel to the coordinate axes and such that contains parallelepip…
A theorem of Besicovitch and a generalization of the Birkhoff Ergodic Theorem
Paul Hagelstein, Daniel Herden, Alexander Stokolos
A remarkable theorem of Besicovitch is that an integrable function on is strongly differentiable if and only if its associated strong maximal function is…