首页|ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR
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In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form L(f)=zfz-(-z)f(-z),where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
Bloch-Landau type theoremBloch constantlinear complex operatorhar-monic mappingbiharmonic mappingunivalent
陈洁玲、刘名生
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School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China
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