The fundamental solution to □ b on quadric manifolds: part 2. Lp regularity and invariant normal forms

Albert Boggess, Andrew Raich

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2 Scopus citations

Abstract

This paper is the second of a multi-part series in which we explore geometric and analytic properties of the Kohn–Laplacian and its inverse on general quadric submanifolds of Cn× Cm. We have two goals in this paper. The first is to give useable sufficient conditions for a map T between quadrics to be a Lie group isomorphism that preserves □ b, and the second is to establish a framework for which appropriate derivatives of the complex Green operator are continuous in Lp and Lp-Sobolev spaces (and hence are hypoelliptic). We apply the general results to codimension two quadrics in C4.

Original languageEnglish (US)
Article number13
JournalComplex Analysis and its Synergies
Volume6
Issue number2
DOIs
StatePublished - Jun 2020

Keywords

  • Complex Green operator
  • Fundamental solution
  • Heisenberg group
  • Quadric submanifolds
  • Szegö kernel
  • Szegö projection
  • Tangential Cauchy–Riemann operator
  • ∂¯

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Numerical Analysis

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