2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122910In this work, we develop $L^p$ boundedness theory for pseudodifferential operators with rough (not even continuous in general) symbols in the $x$ variable. Moreover, the $B(L^p)$ operator norms are estimated explicitly in terms of scale invariant quantities involving the symbols. All the estimates are shown to be sharp with respect to the required smoothness in the $ξ$ variable. As a corollary, we obtain $L^p$ bounds for (smoothed out versions of) the maximal directional Hilbert transform and the Carleson operator.Classical Analysis and ODEsFunctional Analysis47G30, 35S05, 42A45, 42B15text