Browsing Harmonic Analysis by Title
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The Calderón problem with corrupted data
(201701)We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the DirichlettoNeumann map and, therefore, ... 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
(2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ... 
Convergence over fractals for the Schrödinger equation
(202101)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 ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(20181204)Scattering from a nonsmooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ... 
Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on Htype groups
(20210310)Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the subLaplacian on $H$type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 42384294. They concern ... 
Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick
(20211209)We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of DuKimWangZhang. We confirm that the same ... 
A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the InfiniteDimensional Torus
(20200213)In this note we will show a Calder\'onZygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ... 
Degenerate PoincareSobolev inequalities
(2021)Abstract. We study weighted Poincar ́e and Poincar ́eSobolev 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 ... 
Determination of convection terms and quasilinearities appearing in diffusion equations
(201812)We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ... 
Discrete Carleman estimates and three balls inequalities
(20211016)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 ... 
Endpoint estimates, extrapolation for multilinear muckenhoupt classes, and applications
(2019)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 socalled multilinear Muckenhoupt classes. ... 
Extensions of the JohnNirenberg 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 ... 
Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(201911)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the JohnNirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... 
Generalized PoincaréSobolev inequalities
(202012)PoincaréSobolev inequalities are very powerful tools in mathematical analysis which have been extensively used for the study of differential equations and their validity is intimately related with the geometry of the ... 
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 ... 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(20160101)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and fourdimensional cases, this confirms a conjecture of ... 
Hardytype inequalities for fractional powers of the DunklHermite operator
(2018)We prove Hardytype inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use hharmonic expansions to reduce the ... 
HölderLebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
(2018)We study the equations $ \partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $ \partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ... 
Improved A1 − A∞ and related estimates for commutators of rough singular integrals
(2017)An $A_1A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...