Boundedness and concentration of random singular integrals defined by wavelet summability kernels

Abstract

We use Cramér-Chernoff type estimates in order to study the Calderón-Zygmund structure of the kernels ${\sum }_{I\in \mathcal{D}}{a}_I(\omega ){\psi }_I(x){\psi }_I(y)$ where $a_I$ are subgaussian independent random variables and $\{{\psi }_I:I\in \mathcal{D}\}$ is a wavelet basis where $\mathcal{D}$ are the dyadic intervals in $\mathbb{R}$. We consider both, the cases of standard smooth wavelets and the case of the Haar wavelet.

16 pages