Browsing Harmonic Analysis by Issue Date
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Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(Colloquium Mathematicum, 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]. 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 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 ... 
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 ... 
Quantitative weighted mixed weaktype inequalities for classical operators
(Indiana University Mathematics Journal, 20160630)We improve on several mixed weak type inequalities both for the HardyLittlewood maximal function and for CalderónZygmund 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, 20160630)We present dimensionfree 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
(AWMSpringer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 20160701)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 offdiagonal MuckenhouptWheeden conjecture
(WSPC Proceedings, 20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ... 
Borderline Weighted Estimates for Commutators of Singular Integrals
(Israel Journal of Mathematics, 20160701)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
(20160701)Quantitative $A_1A_\infty$ 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)
(20160910)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 CalderónZygmund operators and applications
(Revista Matemática Iberoamericana, 20161125)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 LittlewoodPaley $g_{\lambda}^{*}$function
(Journal of Geometric Analysis, 2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite 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 DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Weighted mixed weaktype 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 CalderónZygmund operators
(Advances in Mathematics, 2017)In recent years, it has been well understood that a CalderónZygmund 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 $A_1A_\infty$ 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 ... 
The Calderón problem with corrupted data
(Inverse Problems, 201701)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 DirichlettoNeumann map and, therefore, ... 
Quantitative weighted estimates for rough homogeneous singular integrals
(Israel Journal of Mathematics, 20170311)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, 20170401)In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the socalled multilinear $L^{r}$Hörmander condition, then $T$ can be dominated by multilinear sparse operators. 
A quantitative approach to weighted Carleson condition
(Concrete Operators, 20170505)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 ...