Browsing Harmonic Analysis by Title
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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 ... 
Extrapolation in general quasiBanach function spaces
(20231115)In this work we prove offdiagonal, limited range, multilinear, vectorvalued, and twoweight versions of the Rubio de Francia extrapolation theorem in general quasiBanach function spaces. We prove mapping properties of ... 
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 ... 
The Hajłasz capacity density condition is selfimproving
(2021)We prove a selfimprovement property of a capacity density condition for a nonlocal Haj lasz gradient in complete geodesic spaces. The proof relates the capacity density condition with boundary Poincar´e inequalities, ... 
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 ... 
Improved fractional Poincaré type inequalities in John domains
(2019)We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ... 
Inverse scattering for a random potential
(201605)In this paper we consider an inverse problem for the $n$dimensional random Schrödinger equation $(\Deltaq+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... 
Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group
(20221104)We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and LittlewoodPaley ... 
Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres
(20230101)We establish an asymptotic formula for the number of lattice points in the sets Sh1,h2,h3(λ):={x∈Z+3:⌊h1(x1)⌋+⌊h2(x2)⌋+⌊h3(x3)⌋=λ} with λ∈Z+; where functions h1, h2, h3 are constant multiples of regularly varying functions ... 
Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
(2020)We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ... 
Maximal operators on the infinitedimensional torus
(20220331)We study maximal operators related to bases on the infinitedimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite expansions
(2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(20160101)In this paper we study mixed weighted weaktype inequal ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2].