Some weak type estimates for cone multipliers

Abstract

We consider operators $T^{\delta}$ associated with a localized height of cone multipliers. It is shown that $T^{\delta}$ is of weak type $(p,p)$ for the functions of the form $f(x,t)=g(|x|,t)$ if $p = 2n/(n +1+2\delta)$, $0 \lt \delta \lt (n- 1)/2$.