대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제31권3호
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  • Pages.533-547
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  • 2016
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY

  • 투고 : 2015.10.24
  • 발행 : 2016.07.31
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초록

In this paper, a generalized boundary version of $Carath{\acute{e}}odory^{\prime}s$ inequality for holomorphic function satisfying $f(z)= f(0)+a_pz^p+{\cdots}$, and ${\Re}f(z){\leq}A$ for ${\mid}z{\mid}$<1 is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime}(c)$ at the point c with ${\Re}f(c)=A$. The sharpness of these estimates is also proved.

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참고문헌

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