TY - JOUR

T1 - Sharp and maximized real-part estimates for derivatives of analytic functions in the disk

AU - Kresin, Gershon

PY - 2013

Y1 - 2013

N2 - Representations for the sharp coefficient in an estimate of the modulus of the n-th derivative of an analytic function in the unit disk D are obtained. It is assumed that the boundary value of the real part of the function on ∂D belongs to Lp. The maximum of a bounded factor in the representation of the sharp coefficient is found. Thereby, a pointwise estimate of the modulus of the n-th derivative of an analytic function in 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 ε (1, ∞), as the product of monotonic functions of |z|.

AB - Representations for the sharp coefficient in an estimate of the modulus of the n-th derivative of an analytic function in the unit disk D are obtained. It is assumed that the boundary value of the real part of the function on ∂D belongs to Lp. The maximum of a bounded factor in the representation of the sharp coefficient is found. Thereby, a pointwise estimate of the modulus of the n-th derivative of an analytic function in 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 ε (1, ∞), as the product of monotonic functions of |z|.

KW - Analytic functions

KW - Estimates for derivatives

KW - Real-part theorems

UR - http://www.scopus.com/inward/record.url?scp=84878870098&partnerID=8YFLogxK

U2 - 10.4171/RLM/646

DO - 10.4171/RLM/646

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AN - SCOPUS:84878870098

SN - 1120-6330

VL - 24

SP - 95

EP - 110

JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni

IS - 1

ER -