Norms of powers of absolutely convergent Fourier series: an example

Charles Henry Heiberg

Vol. 66 (1976), No. 1, 131–152

DOI: 10.2140/pjm.1976.66.131

Abstract

Let f be defined on T² and have an absolutely convergent Fourier series

Set ∥f∥ = ∑ |f_m| and ∥f∥₂² = ∑ |f_m|². In this paper the asymptotic behavior of ∥f^k∥, as k →∞, is studied.

Mathematical Subject Classification

Primary: 42A92, 42A92

Milestones

Received: 14 February 1975

Published: 1 September 1976