## Abstract

In this note, a very general theorem of the CR Hartogs type is proved for almost generic strictly convex domains in C^{n} with real analytic boundary. Given such a domain D, and given an L^{p} function f on ∂D which has holomorphic extensions on the slices of D by complex lines parallel to the coordinate axes, f must be CR—i.e. f has a holomorphic extension to D which is in the Hardy space H^{p}(D). This is the first general result of CR Hartogs type which is not for the ball, or some other domain with symmetries, and holds for L^{1} functions. As a corollary, the Szegő kernel is shown to be the strong operator limit of (π1π2)n, where π_{i} is the projection onto z_{i} holomorphically extendible L^{2}(∂D) functions (in C^{2}, with a slightly more complicated formula in C^{n}).

Original language | English |
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Pages (from-to) | 401-414 |

Number of pages | 14 |

Journal | Mathematische Zeitschrift |

Volume | 288 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Feb 1 2018 |

## ASJC Scopus subject areas

- Mathematics(all)