22 citations · 59 across the 20 of their papers we have counts for
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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…
Abstract Left-Definite Theory: A Model Operator Approach, Examples, Fractional Sobolev Spaces, and Interpolation Theory
Christoph Fischbacher, Fritz Gesztesy, Paul Hagelstein +1
We use a model operator approach and the spectral theorem for self-adjoint operators in a Hilbert space to derive the basic results of abstract left-definite theory in a straightfo…
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…