We establish L p regularity for the Szegö and Bergman projections associated to a simply connected planar domain in any of the following classes: vanishing chord arc; Lipschitz; Ahlfors-regular; or local graph (for the Szegö projection to be well defined, the local graph curve must be rectifiable). As applications, we obtain L p regularity for the Riesz transforms, as well as Sobolev space regularity for the non-homogeneous Dirichlet problem associated to any of the domains above and, more generally, to an arbitrary proper simply connected domain in the plane. © 2004 Mathematica Josephina, Inc.
Szegö and Bergman projections on non-smooth planar domains / Lanzani L.; Stein E.M.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - ELETTRONICO. - 14:1(2004), pp. 63-86. [10.1007/BF02921866]
Szegö and Bergman projections on non-smooth planar domains
Lanzani L.;
2004
Abstract
We establish L p regularity for the Szegö and Bergman projections associated to a simply connected planar domain in any of the following classes: vanishing chord arc; Lipschitz; Ahlfors-regular; or local graph (for the Szegö projection to be well defined, the local graph curve must be rectifiable). As applications, we obtain L p regularity for the Riesz transforms, as well as Sobolev space regularity for the non-homogeneous Dirichlet problem associated to any of the domains above and, more generally, to an arbitrary proper simply connected domain in the plane. © 2004 Mathematica Josephina, Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.