P. Hagelstein

collaborators

3 papers

math.CA2025

Remarks on the construction of $K_{I ¨} $ sets associated to trees not satisfying a separation condition

Paul Hagelstein, Blanca Radillo-Murguia, Alex Stokolos

$K_{I ¨} $ sets involving sticky maps $I ¨ $ have been used in the theory of differentiation of integrals to probabilistically construct Kakeya-type sets that imply certain types of dire…

math.CA2025

Probabilistic Construction of Kakeya-Type Sets in $R^{2}$ associated to separated sets of directions

Paul Hagelstein, Blanca Radillo-Murguia, Alexander Stokolos

We provide a condition on a set of directions $I^c ◯ \subset S^{1}$ ensuring that the associated directional maximal operator $M_{I^} c ◯$ is unbounded on $L^{p} (R^{2})$ for ever…

math.CA2025

Variation of the one-dimensional centered maximal operator on simple functions with gaps between pieces

Paul Hagelstein, Dariusz Kosz, Krzysztof Stempak

Let $M$ denote the centered Hardy--Littlewood operator on $R$ . We prove that \[ {\rm Var} (Mf)\le {\rm Var} (f) - \frac12\big| |f(\infty)|-|f(-\infty)|\big| \] for piecewi…

Remarks on the construction of KI¨​ sets associated to trees not satisfying a separation condition

Probabilistic Construction of Kakeya-Type Sets in R2 associated to separated sets of directions

Variation of the one-dimensional centered maximal operator on simple functions with gaps between pieces

Remarks on the construction of $K_{I ¨} $ sets associated to trees not satisfying a separation condition

Probabilistic Construction of Kakeya-Type Sets in $R^{2}$ associated to separated sets of directions