P. Hagelstein

activity

20122026

most citedTauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases

22 citations · 59 across the 20 of their papers we have counts for

collaborators

24 papers

math.CA2026

Covering lemmas associated to maximal operators of weak type

Paul Hagelstein, Fedor Nazarov, Blanca Radillo-Murguia

Building on the work of A. Córdoba and R. Fefferman, we provide a necessary and sufficient covering condition on a basis $B$ on a separable metric space $X$ with a Borel…

math.CA2024

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

Paul Hagelstein, Blanca Radillo-Murguia, Alex Stokolos

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

math.SP2024

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…

math.CA2024

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…

math.CA2024

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 $Ω \subset S^{1}$ ensuring that the associated directional maximal operator $M_{Ω}$ is unbounded on $L^{p} (R^{2})$ for every…

math.CA2022

Sharp Weak Type Estimates for Maximal Operators associated to Rare Bases

Paul Hagelstein, Giorgi Oniani, Alex Stokolos

Let $B$ denote a nonempty translation invariant collection of intervals in $R^{n}$ (which we regard as a rare basis), and define the associated geometric maximal o…

math.CA2022

$L^{p} (R^{2})$ bounds for geometric maximal operators associated to homothecy invariant convex bases

Paul Hagelstein, Alex Stokolos

Let $B$ be a nonempty homothecy invariant collection of convex sets of positive finite measure in $R^{2}$ . Let $M_{B}$ be the geometric maximal operator de…

math.AP2021

Sharp Weak Type Estimates for a Family of Zygmund Bases

Paul Hagelstein, Alex Stokolos

Let $B$ be a collection of rectangular parallelepipeds in $R^{3}$ whose sides are parallel to the coordinate axes and such that $B$ consists of parallele…

math.CA2021

Sharp weak type estimates for a family of Soria bases

Dmitriy Dmitrishin, Paul Hagelstein, Alex Stokolos

Let $B$ be a collection of rectangular parallelepipeds in $R^{3}$ whose sides are parallel to the coordinate axes and such that $B$ contains parallelepip…

math.CA2020★ 3 cited

Directional square functions

Natalia Accomazzo, Francesco Di Plinio, Paul Hagelstein +2

Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this a…

math.CA2019

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 $f$ on $R^{2}$ is strongly differentiable if and only if its associated strong maximal function $M_{S} f$ is…

math.DS2018

Fejer Polynomials and Control of Nonlinear Discrete Systems

Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova +2

We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consid…

math.CA2017★ 1 cited

Tauberian constants associated to centered translation invariant density bases

Paul A. Hagelstein, Ioannis Parissis

This paper provides a necessary and sufficient condition on Tauberian constants associated to a centered translation invariant differentiation basis so that the basis is a density…

math.CA2016★ 2 cited

Hölder continuity of Tauberian constants associated with discrete and ergodic strong maximal operators

Paul A. Hagelstein, Ioannis Parissis

This paper concerns the smoothness of Tauberian constants of maximal operators in the discrete and ergodic settings. In particular, we define the discrete strong maximal operator $…

math.CA2016

Sharp inequalities for one-sided Muckenhoupt weights

Paul A. Hagelstein, Ioannis Parissis, Olli Saari

Let $A_{\infty}^{+}$ denote the class of one-sided Muckenhoupt weights, namely all the weights $w$ for which $M^{+} : L^{p} (w) \to L^{p, \infty} (w)$ for some $p > 1$ , where $\mathsf M^+…

math.CA2015

Solyanik estimates in ergodic theory

Paul A. Hagelstein, Ioannis Parissis

Let $U_{1}, \dots, U_{n}$ be a collection of commuting measure preserving transformations on a probability space $(Ω, Σ, μ)$ . Associated with these measure preserving transformations…

math.CA2015

A note on local Hölder continuity of weighted Tauberian functions

Paul A. Hagelstein, Ioannis Parissis

Let $M$ and $M_{S}$ respectively denote the Hardy-Littlewood maximal operator with respect to cubes and the strong maximal operator on $R^{n}$ , and…

math.OC2015

On the stability of cycles by delayed feedback control

D. Dmitrishin, P. Hagelstein, A. Khamitova +1

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for sta…

math.CA2014★ 11 cited

Weighted Solyanik estimates for the strong maximal function

Paul A. Hagelstein, Ioannis Parissis

Let $M_{S}$ denote the strong maximal operator on $R^{n}$ and let $w$ be a non-negative, locally integrable function. For $α \in (0, 1)$ we define the weighted s…

math.CA2014★ 6 cited

Solyanik estimates and local Hölder continuity of halo functions of geometric maximal operators

Paul A. Hagelstein, Ioannis Parissis

Let $B$ be a homothecy invariant basis consisting of convex sets in $R^{n}$ , and define the associated geometric maximal operator $M_{B}$ by $$ M_{\mathc…

math.CA2014★ 14 cited

Weighted Solyanik Estimates for the Hardy-Littlewood maximal operator and embedding of $A_{\infty}$ into $A_{p}$

Paul A. Hagelstein, Ioannis Parissis

Let $w$ denote a weight in $R^{n}$ which belongs to the Muckenhoupt class $A_{\infty}$ and let $M_{w}$ denote the uncentered Hardy-Littlewood maximal operator defined w…

math.CA2013

Solyanik estimates in harmonic analysis

Paul A. Hagelstein, Ioannis Parissis

Let $B$ denote a collection of open bounded sets in $R^{n}$ , and define the associated maximal operator $M_{B}$ by $$ M_{\mathcal{B}}f(x) := \sup_{x \in…

math.CA2013★ 22 cited

Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases

Paul A. Hagelstein, Teresa Luque, Ioannis Parissis

We give an alternative characterization of the class of Muckenhoupt weights $A_{\infty, B}$ for homothecy invariant Muckenhoupt bases $B$ consisting of convex s…

math.FA2012

Continuity of halo functions associated to homothecy invariant density bases

Oleksandra V. Beznosova, Paul A. Hagelstein

Let $B$ be a collection of open sets in $R^{n}$ such that, for any $x \in R^{n}$ , there exists a set $U \in B$ of arbitrarily small diameter {…

Covering lemmas associated to maximal operators of weak type

Remarks on the construction of Kσ​ sets associated to trees not satisfying a separation condition

Abstract Left-Definite Theory: A Model Operator Approach, Examples, Fractional Sobolev Spaces, and Interpolation Theory

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

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

Sharp Weak Type Estimates for Maximal Operators associated to Rare Bases

Lp(R2) bounds for geometric maximal operators associated to homothecy invariant convex bases

Sharp Weak Type Estimates for a Family of Zygmund Bases

Sharp weak type estimates for a family of Soria bases

Directional square functions

A theorem of Besicovitch and a generalization of the Birkhoff Ergodic Theorem

Fejer Polynomials and Control of Nonlinear Discrete Systems

Tauberian constants associated to centered translation invariant density bases

Hölder continuity of Tauberian constants associated with discrete and ergodic strong maximal operators

Sharp inequalities for one-sided Muckenhoupt weights

Solyanik estimates in ergodic theory

A note on local Hölder continuity of weighted Tauberian functions

On the stability of cycles by delayed feedback control

Weighted Solyanik estimates for the strong maximal function

Solyanik estimates and local Hölder continuity of halo functions of geometric maximal operators

Weighted Solyanik Estimates for the Hardy-Littlewood maximal operator and embedding of A∞​ into Ap​

Solyanik estimates in harmonic analysis

Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases

Continuity of halo functions associated to homothecy invariant density bases

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

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

$L^{p} (R^{2})$ bounds for geometric maximal operators associated to homothecy invariant convex bases

Weighted Solyanik Estimates for the Hardy-Littlewood maximal operator and embedding of $A_{\infty}$ into $A_{p}$