170 citations · 1.4k across the 61 of their papers we have counts for
63 papers
Characterizations of Lyapunov domains in terms of Riesz transforms and the Plemelj-Privalov theorem
Juan José Marín, José María Martell, Dorina Mitrea +1
We prove several characterizations of -domains (aka Lyapunov domains), where is a growth function satisfying natural assumptions. For example, given an Ahlfo…
Solvability of the Dirichlet problem for the heat equation implies parabolic uniform rectifiability
Simon Bortz, Steven Hofmann, José María Martell +1
Let be an open set in space-time with boundary . Under minimal and natural background assumptions - namely, that is time-symmetricall…
Elliptic operators in rough sets, and the Dirichlet problem with boundary data in Hölder spaces
Mingming Cao, Pablo Hidalgo-Palencia, José María Martell +2
In this paper we study the Dirichlet problem for real-valued second order divergence form elliptic operators with boundary data in Hölder spaces. Our context is that of open sets $…
A note on Rubio de Francia's extrapolation in tent spaces and applications
José María Martell, Pierre Portal
The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt w…
Solvability of the Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph
Simon Bortz, Steven Hofmann, José María Martell +1
We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic weight with respect to surface measure (w…
Carleson measure estimates, corona decompositions, and perturbation of elliptic operators without connectivity
Mingming Cao, Pablo Hidalgo-Palencia, José María Martell
Let be an open set with Ahlfors-David regular boundary satisfying the corkscrew condition. When is connected in some quantitative form one can establish that for any real e…
The regularity problem for degenerate elliptic operators in weighted spaces
Pascal Auscher, Li Chen, José María Martell +1
We study the solvability of the regularity problem for degenerate elliptic operators in the block case for data in weighted spaces. More precisely, let be a degenerate ellipt…
Square function and non-tangential maximal function estimates for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
Murat Akman, Steve Hofmann, José María Martell +1
Let , , be a 1-sided non-tangentially accessible domain (aka uniform domain), that is, satisfies the interior Corkscrew and Harnack chain cond…
Extrapolation on function and modular spaces, and applications
Mingming Cao, Juan José Marín, José María Martell
We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted…
On the condition for elliptic operators in 1-sided NTA domains satisfying the capacity density condition
Mingming Cao, Óscar Domínguez, José María Martell +1
Let , , be a 1-sided non-tangentially accessible domain (i.e., quantitatively open and path-connected) satisfiying the capacity density condition…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of w…
Elliptic measures and Square function estimates on 1-sided chord-arc domains
Mingming Cao, José María Martell, Andrea Olivo
In nice environments, such as Lipschitz or chord-arc domains, it is well-known that the solvability of the Dirichlet problem for an elliptic operator in , for some finite ,…
Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates
Juan Cavero, Steve Hofmann, José María Martell +1
We generalize to the setting of 1-sided chord-arc domains, that is, to domains satisfying the interior Corkscrew and Harnack Chain conditions (these are respectively scale-invarian…
The regularity problem for uniformly elliptic operators in weighted spaces
Li Chen, José María Martell, Cruz Prisuelos-Arribas
This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the bou…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a…
Harmonic measure and quantitative connectivity: geometric characterization of the -solvability of the Dirichlet problem
Jonas Azzam, Steve Hofmann, José María Martell +2
It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak- property) of harmonic measure with respect to surface measure, on the b…
Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains
Steve Hofmann, José María Martell, Svitlana Mayboroda
In relatively nice geometric settings, in particular, on Lipschitz domains, absolute continuity of elliptic measure with respect to the surface measure is equivalent to Carleson me…
Fatou-Type Theorems and Boundary Value Problems for Elliptic Systems in the Upper Half-Space
José María Martell, Dorina Mitrea, Irina Mitrea +1
We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-spa…
End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
Kangwei Li, José María Martell, Henri Martikainen +2
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so…
Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
Murat Akman, Steve Hofmann, José María Martell +1
Let , , be a 1-sided non-tangentially accessible domain (aka uniform domain), i.e., a set which satisfies the interior Corkscrew and Harnack chain…
The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
Juan José Marín, José María Martell, Marius Mitrea
We prove well-posedness results for the Dirichlet problem in for homogeneous, second order, constant complex coefficient elliptic systems with boundary data in…
Extrapolation for multilinear Muckenhoupt classes and applications to the bilinear Hilbert transform
Kangwei Li, José María Martell, Sheldy Ombrosi
In this paper we solve a long standing problem about the multivariable Rubio de Francia extrapolation theorem for the multilinear Muckenhoupt classes , which were exte…
Harmonic measure and quantitative connectivity: geometric characterization of the -solvability of the Dirichlet problem. Part I
Steve Hofmann, José María Martell
Let be an open set, not necessarily connected, with an -dimensional uniformly rectifiable boundary. We show that may be approximated in a…
Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach
Árpád Bényi, José María Martell, Kabe Moen +2
We present a unified method to obtain weighted estimates of linear and multilinear commutators with BMO functions, that is amenable to a plethora of operators and functional settin…