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The Szegö projection on convex domains

The Szegö projection on convex domains Math. Z. 224, 519{553 (1997) The Szego projection on convex domains 1 2 J.D. McNeal , E.M. Stein Dept. of Mathematics, Ohio State University, Columbus, OH 43210-1174, USA Dept. of Mathematics, Princeton University, Princeton, NJ 08544, USA Received 25 September 1995; in nal form 21 November 1995 Introduction The purpose of this paper is to study the Szego projection operator for a smoothly bounded convex domain of nite type in C . The results ob- tained are two-fold. First, the (essentially sharp) di erential inequalities sat- is ed by the Szego kernel are established. Second, sharp Sobolev space and Lipschitz space estimates for the projection operator are proved. The function space estimates in question are both isotropic (for the usual L (b ) Sobolev spaces and the classical  (b ) Lipschitz spaces), and non-isotropic, i.e., for (b ) Lipschitz spaces de ned in terms of the geometry of the bound- certain ary of This article is the second in a series, the rst, [McS], having dealt with some analogous questions of Sobolev and Lipschitz estimates for the Bergman projection. At the basis of our analysis in both papers are certain geometric constructions for convex domains of nite type http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

The Szegö projection on convex domains

McNeal, J. D.; Stein, E. M.
Mathematische Zeitschrift , Volume 224 (4) – Apr 18, 1997
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References (15)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/PL00004593
Publisher site
See Article on Publisher Site

Abstract

Math. Z. 224, 519{553 (1997) The Szego projection on convex domains 1 2 J.D. McNeal , E.M. Stein Dept. of Mathematics, Ohio State University, Columbus, OH 43210-1174, USA Dept. of Mathematics, Princeton University, Princeton, NJ 08544, USA Received 25 September 1995; in nal form 21 November 1995 Introduction The purpose of this paper is to study the Szego projection operator for a smoothly bounded convex domain of nite type in C . The results ob- tained are two-fold. First, the (essentially sharp) di erential inequalities sat- is ed by the Szego kernel are established. Second, sharp Sobolev space and Lipschitz space estimates for the projection operator are proved. The function space estimates in question are both isotropic (for the usual L (b ) Sobolev spaces and the classical  (b ) Lipschitz spaces), and non-isotropic, i.e., for (b ) Lipschitz spaces de ned in terms of the geometry of the bound- certain ary of This article is the second in a series, the rst, [McS], having dealt with some analogous questions of Sobolev and Lipschitz estimates for the Bergman projection. At the basis of our analysis in both papers are certain geometric constructions for convex domains of nite type

Journal

Mathematische Zeitschrift – Springer Journals

Published: Apr 18, 1997

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