Growth and coefficient estimates for uniformly locally univalent functions on the unit disk

Yong Chang Kim; Toshiyuki Sugawa

doi:10.1216/rmjm/1030539616

Growth and coefficient estimates for uniformly locally univalent functions on the unit disk

Yong Chang Kim, Toshiyuki Sugawa

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

38 Citations (Scopus)

Abstract

In this note we shall give a sharpd istortion estimate for a uniformly locally univalent holomorphic function on the unit disk in terms of the norm of pre-Schwarzian derivative. As applications, we shall investigate the growth of coefficients and integral means of such a function and mention a connection with Hardy spaces. We also give norm estimates for typical classes of univalent functions.

Original language	English
Pages (from-to)	179-200
Number of pages	22
Journal	Rocky Mountain Journal of Mathematics
Volume	32
Issue number	1
DOIs	https://doi.org/10.1216/rmjm/1030539616
Publication status	Published - 2002
Externally published	Yes

Keywords

Coefficient estimate
Growth estimate
Pre-Schwarzian derivative
Uniformly locally univalent

ASJC Scopus subject areas

Mathematics(all)

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10.1216/rmjm/1030539616

Cite this

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abstract = "In this note we shall give a sharpd istortion estimate for a uniformly locally univalent holomorphic function on the unit disk in terms of the norm of pre-Schwarzian derivative. As applications, we shall investigate the growth of coefficients and integral means of such a function and mention a connection with Hardy spaces. We also give norm estimates for typical classes of univalent functions.",

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AU - Sugawa, Toshiyuki

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AB - In this note we shall give a sharpd istortion estimate for a uniformly locally univalent holomorphic function on the unit disk in terms of the norm of pre-Schwarzian derivative. As applications, we shall investigate the growth of coefficients and integral means of such a function and mention a connection with Hardy spaces. We also give norm estimates for typical classes of univalent functions.

KW - Coefficient estimate

KW - Growth estimate

KW - Pre-Schwarzian derivative

KW - Uniformly locally univalent

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DO - 10.1216/rmjm/1030539616

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JF - Rocky Mountain Journal of Mathematics

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ER -

Growth and coefficient estimates for uniformly locally univalent functions on the unit disk

Abstract

Keywords

ASJC Scopus subject areas

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