• Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates 

  Li K.; Ombrosi S.; Pérez C. (Mathematische Annalen, 2018-09)

  We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...

• On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids 

  Scrobogna S. (Journal of Differential Equations, 2018-09)

  We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...

• Weighted norm inequalities for rough singular integral operators 

  Li K.; Pérez C.; Rivera-Ríos I.; Roncal L. (Journal of Geometric Analysis, 2018-08-17)

  In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...

• Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach 

  Canevari G.; Segatti A. (Archive for Rational Mechanics and Analysis, 2018-07)

  In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...

• On the regularity of solutions to the k-generalized korteweg-de vries equation 

  Kenig C.E.; Linares F.; Ponce G.; Vega L. (Proceedings of the American Mathematical Society, 2018-07)

  This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...

• Absence of eigenvalues of two-dimensional magnetic Schroedinger operators 

  Fanelli L.; Krejcirik D.; Vega L. (2018-01-01)

  By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...

• Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation 

  Correia S.; Côte R.; Vega L. (2018-07-06)

  We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...

• On the improvement of the Hardy inequality due to singular magnetic fields 

  Fanelli L.; Krejcirik D.; Laptev A.; Vega L. (2018-07-12)

  We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...

• Regularity of fractional maximal functions through Fourier multipliers 

  Beltran D.; Ramos J. P.; Saari O. (2018)

  We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ...

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds 

  Beltran D.; Hickman J.; Sogge C. D. (2018)

  The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...

• Sparse bounds for pseudodifferential operators 

  Beltran D.; Cladek L. (Journal d'Analyse Mathématique, 2018)

  We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...

• Spectral stability of Schrödinger operators with subordinated complex potentials 

  Fanelli L.; Krejcirik D.; Vega L. (Journal of Spectral Theory, 2018-06-28)

  We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...

• On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation 

  De la Hoz F.; Vega L. (Journal of Nonlinear Science, 2018-06-28)

  In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...

• Sharp exponential localization for eigenfunctions of the Dirac Operator 

  Cassano B. (2018)

  We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ...

• On Bloom type estimates for iterated commutators of fractional integrals 

  Accomazzo N.; Martínez-Perales J.C.; Rivera-Ríos I.P. (Indiana University Mathematics Journal, 2018-04)

  In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. We give new proofs for those inequalities relying upon a new sparse ...

• Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials 

  Cassano B.; Pizzichillo F. (Letters in Mathematical Physics, 2018)

  We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...

• Quantitative weighted estimates for singular integrals and commutators 

  Rivera-Ríos I.P. (2018-02-27)

  In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...

• Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities 

  Liang S.; Zheng S. (Nonlinear Analysis, 2018-02-15)

  We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...

• Zero limit of entropic relaxation time for the Shliomis model of ferrofluids 

  Scrobogna S. (2018-02-11)

  We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $ \tau \in (0, \tau_0) $. This allows us to study the convergence when $ \tau\to 0 $ for such solutions.

• Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients 

  Zheng S.; Tian H. (Boundary Value Problems, 2017)

  We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ...

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