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EnglishWe 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.
| Titolo: | Szegö and Bergman projections on non-smooth planar domains | |
| Autore/i: | Lanzani L.; Stein E. M. | |
| Autore/i Unibo: | ||
| Anno: | 2004 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/BF02921866 | |
| 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. | |
| Data stato definitivo: | 2022-02-28T15:43:22Z | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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