Journal of the Australian Mathematical Society  Series A
Vol. 65 Part 1 (1998)
Integral means on radially weighted spaces of analytic functions
Mats Erik Andersson
Department of Mathematics
Kungliga Tekniska Högskolan
Lindstedtsvägen 25
S100 44 Stockholm
Sweden
email: matsa@math.kth.se
Current address:
Department of Mathematics
University of Stockholm
S106 91 Stockholm
Sweden
email: mats.andersson@matematik.su.se
Abstract:
Hilbert spaces of analytic functions generated by rotationally symmetric
measures on disks and annuli are studied. A domination relation between
function norm and weighted sums of integral means on circles is developed.
The function norm and the weighted sum take the same value for a specified
class of polynomials. This class can be varied according to two parameters.
Parts of the construction carry over to other Banach spaces of analytic or
harmonic functions. Counterexamples illuminating properties of the
complex method of interpolation appear as a byproduct.
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