TY - JOUR
T1 - Growth and coefficient estimates for uniformly locally univalent functions on the unit disk
AU - Kim, Yong Chang
AU - Sugawa, Toshiyuki
PY - 2002
Y1 - 2002
N2 - 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.
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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U2 - 10.1216/rmjm/1030539616
DO - 10.1216/rmjm/1030539616
M3 - Article
AN - SCOPUS:0036520899
SN - 0035-7596
VL - 32
SP - 179
EP - 200
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 1
ER -