On isometries of hardy spaces on compact abelian groups

Junichi Tanaka

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Abstract

Let Hp(m),<0 p ≦ ∞, be the Hardy spaces on a quotient K of the Bohr group. In this paper we completely determine the isometries of Hp(m), p ≠ 2, onto itself. Our result is a generalization of a recent work of Muhly who determined the isometries of Hp(m) onto itself under the assumption that the dual group of K is countable, and it may be regarded as a partial answer to a question posed by Muhly.

Original languageEnglish
Pages (from-to)219-232
Number of pages14
JournalPacific Journal of Mathematics
Volume95
Issue number1
Publication statusPublished - 1981
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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