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

Research output: Contribution to journalArticle

7 Citations (Scopus)

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

Fingerprint

Degenerate Elliptic Operators
Pseudoconvex Domain
Hardy Space
Unit Disk
Isomorphic
Bergman Metric
BMO Space
Laplace-Beltrami Operator
Dual space
Topological Properties
Elliptic Operator
Analytic function
Corollary

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Degenerate elliptic operators, hardy spaces and diffusions on strongly pseudoconvex domains. / Arai, Hitoshi.

In: Tohoku Mathematical Journal, Vol. 46, No. 4, 01.01.1994, p. 469-498.

Research output: Contribution to journalArticle

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