Sharp real-part theorems for high order derivatives
2012 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 181, no 2, 107-125 p.Article in journal (Refereed) Published
We obtain a representation for the sharp coefficient in an estimate of the modulus of the nth derivative of an analytic function in the upper half-plane C + . It is assumed that the boundary value of the real part of the function on ∂C + belongs to Lp. This representation is specified for p = 1 and p = 2. For p = ∞ and for derivatives of odd order, an explicit formula for the sharp coefficient is found. A limit relation for the sharp coefficient in a pointwise estimate for the modulus of the n-th derivative of an analytic function in a disk is found as the point approaches the boundary circle. It is assumed that the boundary value of the real part of the function belongs to Lp. The relation in question contains the sharp constant from the estimate of the modulus of the n-th derivative of an analytic function in C + . As a corollary, a limit relation for the modulus of the n-th derivative of an analytic function with the bounded real part is obtained in a domain with smooth boundary.
Place, publisher, year, edition, pages
Springer, 2012. Vol. 181, no 2, 107-125 p.
IdentifiersURN: urn:nbn:se:liu:diva-89712DOI: 10.1007/s10958-012-0679-5OAI: oai:DiVA.org:liu-89712DiVA: diva2:609151