Cauchy integral equalities and applications

Boo Rim Choe

doi:10.1090/S0002-9947-1989-0935531-9

Cauchy integral equalities and applications

Boo Rim Choe

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study bounded holomorphic functions n on the unit ball B_nof C satisfying the following so-called Cauchy integral equalities:for some sequence λ_mdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on B_n, a projection theorem about the orthogonal projection of H²(B_n) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(B_n) as the dual of H¹(B_n), then the map g → g o π is a linear isometry of BMOA(B₁) into BMOA(B_n) for every inner function π on B_nsuch that π(0) = 0.

Original language	English
Pages (from-to)	337-352
Number of pages	16
Journal	Transactions of the American Mathematical Society
Volume	315
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1989-0935531-9
Publication status	Published - 1989 Sept
Externally published	Yes

Keywords

Cauchy Integral Equalities
Projection
The Ahern-Rudin problem

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0002-9947-1989-0935531-9

Cite this

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abstract = "We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.",

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AU - Choe, Boo Rim

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N2 - We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.

AB - We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.

KW - Cauchy Integral Equalities

KW - Projection

KW - The Ahern-Rudin problem

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Cauchy integral equalities and applications

Abstract

Keywords

ASJC Scopus subject areas

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