Degenerate elliptic operators, hardy spaces and diffusions on strongly pseudoconvex domains

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Abstract

We will study some linear topological properties of Hardy space H1 associated to solutions of the Laplace-Beltrami operator or more general elliptic operators on a smoothly bounded strongly pseudoconvex domain endowed with the Bergman metric. In particular, we characterize such Hardy spaces in terms of diffusions and non-isotropic atoms. Consequently we see that the dual space of H1 is equivalent to the non-isotropic BMO space and that H1 is isomorphic to the classical Hardy space on the open unit disc in the plane. As a corollary we also prove that the Hardy space H1 of holomorphic functions on a strongly pseudoconvex domain is isomorphic to the classical one on the open unit disc, as conjectured by P. Wojtaszczyk.

Original languageEnglish
Pages (from-to)469-498
Number of pages30
JournalTohoku Mathematical Journal
Volume46
Issue number4
DOIs
Publication statusPublished - 1994 Jan 1
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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