25 citations · 58 across the 13 of their papers we have counts for
15 papers
The martingale representation theorem for cylindrical martingale valued measures
S. Cambronero, D. Campos, C. A. Fonseca-Mora +1
We prove a martingale representation theorem for cylindrical martingale-valued measures defined on a separable Banach space. The main tool for establishing the theorem, is a new th…
Markov property and path regularity for the solutions to SPDEs driven by cylindrical-martingale valued measures
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
In this paper we prove the Markov property for the solution to stochastic partial differential equations driven by a cylindrical orthogonal martingale-valued measure. We assume our…
Szemerédi's Theorem Along Cantor Sets of Integers
Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2
Let be Cantor set of integers, that is a set of integers with restricted digits modulo a base , and suppose is one of the restricted digit…
Integer Cantor Sets: Arithmetic Combinatorial Properties
Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2
Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we…
Weighted Weak Type estimates for non-integral Square Functions
Dario Mena, Maria Carmen Reguera, Luz Roncal
We provide quantitative weighted weak type estimates for non-integral square functions in the critical case in terms of the and reverse Hölder constants associated to t…
Itô's Formula for Itô processes defined with respect to a cylindrical-martingale valued measure
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
Using the authors' recently developed stochastic integration [Stoch PDE: Anal Comp, 2024], we prove an Itô formula for Hilbert space-valued Itô processes defined with respect to a…
Riesz spaces of signed charges on semi-rings
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
A constructive definition of the supremum of a family of set functions is exploited in the context of Riesz spaces of signed measures and finitely additive functions (signed charge…
Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
Santiago Cambronero, David Campos, C. A. Fonseca-Mora +1
We develop a theory of Hilbert-space valued stochastic integration with respect to cylindrical martingale-valued measures. As part of our construction, we expand the concept of qua…
A nonlinear relapse model with disaggregated contact rates: analysis of a forward-backward bifurcation
Jimmy Calvo-Monge, Fabio Sanchez, Juan G. Calvo +1
We developed a nonlinear differential equation model to explore the dynamics of relapse phenomena. Our incidence rate function is formulated, taking inspiration from recent adaptiv…
Lacunary Discrete Spherical Maximal Functions
Robert Kesler, Michael T. Lacey, Dario Mena
We prove new bounds for discrete spherical averages in dimensions . We focus on the case of lacunary radii, first for general lacunary radii…
Sparse Bounds for the Discrete Spherical Maximal Function
Robert Kesler, Michael T. Lacey, Darío Mena
We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proo…
Sparse Bounds for Bochner-Riesz Multipliers
Michael T. Lacey, Darío Mena, Maria Carmen Reguera
The Bochner-Riesz multipliers on are shown to satisfy a range of sparse bounds, for all . The range of sparse bounds increases to th…
Sparse Bounds for Discrete Quadratic Phase Hilbert Transform
Robert Kesler, Darío Mena
Consider the discrete quadratic phase Hilbert Transform acting on finitely supported functions We pro…
The Sparse T1 Theorem
Michael T. Lacey, Darío Mena
We impose standard -type assumptions on a Calderón-Zygmund operator , and deduce that for bounded compactly supported functions there is a sparse bilinear form…
Characterization of two parameter matrix-valued BMO by commutator with the Hilbert transform
Darío Mena
In this paper we prove that the space of two parameter, matrix-valued BMO functions can be characterized by considering iterated commutators with the Hilbert transform. Specificall…