A representation of H^p-functions with 0 < p < ∞

Sergio Eduardo Zarantonello

Vol. 79 (1978), No. 1, 271–282

DOI: 10.2140/pjm.1978.79.271

Abstract

Let E be an open arc in the unit circle. Let F belong to the Hardy space H^p, 0 < p < ∞, and let g be the restriction of the boundary distribution of F to E. For each 0 < λ < 1 we construct functions G_λ ∈ H^p from g such that G_λ → F in the topology of H^p as λ → 1.

Mathematical Subject Classification 2000

Primary: 30D55

Secondary: 30E20, 47B35

Milestones

Received: 28 September 1977

Published: 1 November 1978