HYPOELLIPTICITY OF THE KOHN LAPLACIAN FOR THREE-DIMENSIONAL TUBULAR CAUCHY–RIEMANN STRUCTURES

Abstract

A necessary and sufficient geometric condition is established for the Kohn Laplacian to be hypoelliptic, modulo its nullspace, for boundaries of arbitrary infinitely differentiable pseudoconvex tube domains in two complex variables. Hypoellipticity is also proved to be equivalent to validity of a superlogarithmic estimate, for this special class of structures.AMS 2000 Mathematics subject classification: Primary 32W05; 32T27. Secondary 35J70.