Listar Harmonic Analysis por fecha de publicación
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Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 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]. -
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 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 ... -
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 ... -
Quantitative weighted mixed weak-type inequalities for classical operators
(Indiana University Mathematics Journal, 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 ... -
Reverse Hölder Property for Strong Weights and General Measures
(Journal of Geometric Analysis, 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 ... -
Three Observations on Commutators of Singular Integral Operators with BMO Functions
(AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 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\, : ... -
A note on the off-diagonal Muckenhoupt-Wheeden conjecture
(WSPC Proceedings, 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 ... -
Borderline Weighted Estimates for Commutators of Singular Integrals
(Israel Journal of Mathematics, 2016-07-01)In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left|[b,T]f(x)\right| > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\|b\|_{BMO}\f ... -
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(2016-07-01)Quantitative $A_1-A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \|T_\Omega ... -
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(2016-09-10)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... -
New bounds for bilinear Calderón-Zygmund operators and applications
(Revista Matemática Iberoamericana, 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 ... -
A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function
(Journal of Geometric Analysis, 2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ... -
Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions
(Transactions of the American Mathematical Society, 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 ... -
Weighted mixed weak-type inequalities for multilinear operators
(Studia Mathematica, 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 ... -
On pointwise and weighted estimates for commutators of Calderón-Zygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... -
Improved A1 − A∞ and related estimates for commutators of rough singular integrals
(Proceedings of the Edinburgh Mathematical Society, 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 ... -
The Calderón problem with corrupted data
(Inverse Problems, 2017-01)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 Dirichlet-to-Neumann map and, therefore, ... -
Quantitative weighted estimates for rough homogeneous singular integrals
(Israel Journal of Mathematics, 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 ... -
Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition
(Michigan Mathematical Journal, 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. -
A quantitative approach to weighted Carleson condition
(Concrete Operators, 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 ...