= Annularly cancelling singular convolution kernel
{title2=$|K(x)|\leq A|x|^{-d},\quad\int_{r<|x|<R}K(x)\,dx=0$}
A measurable <convolution> kernel satisfying the displayed size and cancellation properties together with the <Hörmander integral kernel condition> defines uniformly bounded Fourier multipliers after deletion of a ball at the origin. The deleted-ball kernels belong to $L^2$, although they need not belong to $L^1$ at infinity. Cancellation controls low-frequency integration near the deleted ball; translation by half an oscillation controls the far tail through the <oscillatory tail estimate for a singular kernel>.
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