Extremal problems for hardy classes of banach-space-valued functions and the geometry of the space of values
Title:
Extremal problems for hardy classes of banach-space-valued functions and the geometry of the space of values
Author:
Peterburgsky, Irina
Appeared in:
Complex variables and elliptic equations
Paging:
Volume 29 (1996) nr. 3 pages 233-247
Year:
1996-04
Contents:
Let Hp(E), 1≤p≤∞, be a Hardy space of analytic functions from an open unit disk of a complex plane to a complex Banach space E. We define a class of linear operators L,L: Hp (E) → E, which are in a certain sense averages of the “boundary values”, and for a given L, study the points of maximum of norm ‖Lf‖, where f lies on the unit sphere. The relationships between the geometry (strong complex convexity) of the unit sphere S:E in E, the general form of extremal functions f ε SHp(E), and their location on SHp(E) are established.
Journal description