$L^p$ estimates with weights for the $\overline\partial$-equation on real ellipsoids in $\Bbb C^n$
Commun. Korean Math. Soc. 2003 Vol. 18, No. 2, 263-280
Printed June 1, 2003
Heungju Ahn
Universita di Padova
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.
Keywords : Cauchy-Riemann equation, $L^p$ estimates, real ellipsoid
MSC numbers : Primary 32A26, 32W05
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