Weak (1,1) bounds for oscillatory singular integrals (Q1117418)

Theorem. For any polynomial P: \({\mathbb{R}}^ n\times {\mathbb{R}}^ n\to {\mathbb{R}}\) and any Calderón-Zygmund kernel K, the operator \(Tf(x)=p.v.\int e^{iP(x,y)}K(x-y)f(y)dy\) is of weak type (1,1) with a bound depending only on \(\| K\|_{CZ}\) and the degree of P. For the proof the authors use a ew variant of the Calderón-Zygmund decomposition method. This variant appears to be of independent interest.