Browsing Harmonic Analysis by Title
Now showing items 59-78 of 79
-
Reconstruction of the Derivative of the Conductivity at the Boundary
Ponce Vanegas, F.
(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
Pérez, C.; Picón, T.; Saari, Olli; Sousa, Mateus (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
Luque, T.; Pérez, C.; Rela, E. (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
Pérez, C.; Rivera-Ríos, I.P. (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 ... -
Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
Ciaurri Ó.; Nowak, A.; Roncal, L. (2018)
We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ... -
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(2018-12)For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ... -
Variation bounds for spherical averages
Beltran, D.; Oberlin, R.; Roncal, L.; Stovall, B.; Seeger, A. (2021-06-22)
We consider variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates -
Vector-valued extensions for fractional integrals of Laguerre expansions
Ciaurri Ó.; Roncal, L. (2018)
We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ... -
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
Cejas, M.E.; Li, K.; Pérez, C.; Rivera-Ríos, I.P. (2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ... -
Weak and strong $A_p$-$A_\infty$ estimates for square functions and related operators
(2017-07)We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... -
Weighted mixed weak-type inequalities for multilinear operators
(2017)In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...