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 ∑I∈DaI(ω)ψI(x)ψI(y), and their concentration about the mean, where aI are subgaussian independent random variables and {ψI:I∈D} is a wavelet basis where D are the dyadic intervals in R. We consider both, the cases of standard smooth wavelets and the case of the Haar wavelet.