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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 ...
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 ...
Borderline Weighted Estimates for Commutators of Singular Integrals
(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 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 ...
$A_1$ 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 ...
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\, : ...
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 ...
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 ...
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 ...
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 ...