Now showing items 27-46 of 79

• #### Generalized Poincaré-Sobolev inequalities ﻿

(2020-12)
Poincaré-Sobolev 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 ﻿

(2016-01-01)
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 four-dimensional cases, this confirms a conjecture of ...
• #### Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator ﻿

(2018)
We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...
• #### Hölder-Lebesgue 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 $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ 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 ﻿

(2016-05)
In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ...
• #### 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 infinite-dimensional torus ﻿

(2022-03-31)
We study maximal operators related to bases on the infinite-dimensional 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 Dunkl-Hermite expansions ﻿

(2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
• #### Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer ﻿

(2016-01-01)
In this paper we study mixed weighted weak-type 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].
• #### Multilinear operator-valued calderón-zygmund theory ﻿

(2020)
We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness ...
• #### Multilinear singular integrals on non-commutative lp spaces ﻿

(2019)
We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...
• #### New bounds for bilinear Calderón-Zygmund operators and applications ﻿

(2016-11-25)
In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ...
• #### Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications ﻿

(2018)
The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ $(-\Delta_h)^su=f,$ for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ...
• #### A note on generalized Fujii-Wilson conditions and BMO spaces ﻿

(2020-07-01)
In this note we generalize the definition of the Fujii-Wilson condition providing quantitative characterizations of some interesting classes of weights, such as A∞, A∞weak and Cp, in terms of BMO type spaces suited to them. ...
• #### A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities ﻿

(2020)
The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent self-improving result of generalized inequalities of Poincar\'e-type in the Euclidean ...
• #### A note on the off-diagonal Muckenhoupt-Wheeden conjecture ﻿

(2016-07-01)
We obtain the off-diagonal Muckenhoupt-Wheeden conjecture for Calderón-Zygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the Hardy-Littlewood maximal function satisfies the following ...
• #### The observational limit of wave packets with noisy measurements ﻿

(2019)
The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian ...