$L^p$ estimates with weights for the $\overline\partial$-equationon real ellipsoids in $\Bbb C^n$

Abstract

We prove weighted $L^p$ estimates with respect to the non-isotropic norm for the $\db$-equation on real ellipsoids, where weights are powers of the distance to the boundary. The non-isotropic norm is smaller than the usual norm, by a factor which is equal to the distance to the boundary in the complex tangential component and which is equal to the $m$-th root of the distance to the boundary in the complex normal component. Here $m$ is the maximal order of contact of the boundary of the real ellipsoid with complex analytic curves.