Now showing items 52-71 of 79

• #### 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 $f\in H^s(\mathbb{R}^n)$ ...
• #### Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates ﻿

(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\, ...
• #### A quantitative approach to weighted Carleson condition ﻿

(2017-05-05)
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator $\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$ are ...
• #### Quantitative weighted estimates for rough homogeneous singular integrals ﻿

(2017-03-11)
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
• #### Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function ﻿

(2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
• #### Quantitative weighted estimates for singular integrals and commutators ﻿

(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 ...
• #### Quantitative weighted mixed weak-type inequalities for classical operators ﻿

(2016-06-30)
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
• #### Reconstruction of the Derivative of the Conductivity at the Boundary ﻿

(2019-08)
We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness ...
• #### Regularity of maximal functions on Hardy–Sobolev spaces ﻿

(2018-12-01)
We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces H1,p(Rd) when p > d/(d + 1). This range of exponents is sharp. As a by-product of the ...
• #### RESTRICTED TESTING FOR POSITIVE OPERATORS ﻿

(2020)
We prove that for certain positive operators T, such as the Hardy-Littlewood maximal function and fractional integrals, there is a constant D>1, depending only on the dimension n, such that the two weight norm inequality ...
• #### Reverse Hölder Property for Strong Weights and General Measures ﻿

(2016-06-30)
We present dimension-free reverse Hölder inequalities for strong $A^{\ast}_p$ weights, $1 \le p < \infty$. We also provide a proof for the full range of local integrability of $A^{\ast}_1$ weights. The common ingredient ...
• #### Rotational smoothing ﻿

(2022-01-05)
Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators ...
• #### Scattering with critically-singular and δ-shell potentials ﻿

(2019)
The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ...
• #### Sharp reverse Hölder inequality for Cp weights and applications ﻿

(2020)
We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen ...
• #### Sharp weighted estimates involving one supremum ﻿

(2017-07)
In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ...
• #### Sparse and weighted estimates for generalized Hörmander operators and commutators ﻿

(2019)
In this paper a pointwise sparse domination for generalized Ho ̈rmander and also for iterated commutators with those operators is provided generalizing the sparse domination result in [24]. Relying upon that sparse domination ...
• #### Sparse bounds for maximal rough singular integrals via the Fourier transform ﻿

(2019-03-12)
We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
• #### Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition ﻿

(2017-04-01)
In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.
• #### Three Observations on Commutators of Singular Integral Operators with BMO Functions ﻿

(2016-07-01)
Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely \$\[\frac{1}{|Q|}\left|\left\{x\in Q\, : ...
• #### Topics in Harmonic Analysis; commutators and directional singular integrals ﻿

(2020-03-01)
This dissertation focuses on two main topics: commutators and maximal directional operators. Our first topic will also distinguish between two cases: commutators of singular integral operators and BMO functions and ...