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Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
(2021-12-09)
We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
Discrete Carleman estimates and three balls inequalities
(2021-10-16)
We prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the ...
Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol
(2021-08-24)
We study the problem of pointwise convergence for equations of the type
$i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular.
We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...
Bilinear Spherical Maximal Functions of Product Type
(2021-08-12)
In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered ...
Variation bounds for spherical averages
(2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates
Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups
(2021-03-10)
Recently we have found a couple of errors in our paper entitled An extension problem
and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res.
Not. IMRN (2020), no. 14, 4238--4294. They concern ...
Degenerate Poincare-Sobolev inequalities
(2021)
Abstract. We study weighted Poincar ́e and Poincar ́e-Sobolev type in- equalities with an explicit analysis on the dependence on the Ap con- stants of the involved weights. We obtain inequalities of the form with different ...
Geometric Harmonic Analysis
(2021)
This thesis is the compilation of the results obtained during my PhD, which started in
January 2018 and is being completed in the end of 2021. The main matter is divided
into ve chapters, Chapters 2 6. Each of these ...
Extensions of the John-Nirenberg theorem and applications
(2021)
The John–Nirenberg theorem states that functions of bounded mean oscillation are
exponentially integrable. In this article we give two extensions of this theorem. The first one
relates the dyadic maximal function to the ...
Convergence over fractals for the Schrödinger equation
(2021-01)
We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the
minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...