JournalsrlmVol. 24, No. 1pp. 95–110

Sharp and maximized real-part estimates for derivatives of analytic functions in the disk

  • Gershon Kresin

    Ariel University Center of Samaria, Israel
Sharp and maximized real-part estimates for derivatives of analytic functions in the disk cover
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Abstract

Representations for the sharp coefficient in an estimate of the modulus of the nn-th derivative of an analytic function in the unit disk D{\mathbb D} are obtained. It is assumed that the boundary value of the real part of the function on D\partial{\mathbb D} belongs to LpL^p. The maximum of a bounded factor in the representation of the sharp coefficient is found. Thereby, a pointwise estimate of the modulus of the nn-th derivative of an analytic function in D{\mathbb D} with a best constant is obtained. The sharp coefficient in the estimate of the modulus of the first derivative in the explicit form is found. This coefficient is represented, for p(1,)p\in (1, \infty), as the product of monotonic functions of z|z|.

Cite this article

Gershon Kresin, Sharp and maximized real-part estimates for derivatives of analytic functions in the disk. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 1, pp. 95–110

DOI 10.4171/RLM/646