Vol. 62, No. 1, 1976

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Composition operators on Hp(A)

David M. Boyd

Vol. 62 (1976), No. 1, 55–60

The space Hp(A) is a generalization of the Hardy space Hp for functions analytic on an annulus A. This paper shows that composition operators are bounded operators on Hp(A) and obtains an upper bound on the norm of the operator. The space H2(A) is given a Hilbert space structure and those composition operators that are in the Hilbert-Schmidt class of operators on H2(A) are characterized in terms of integral properties of the inducing function.

Mathematical Subject Classification 2000
Primary: 47B47
Received: 26 August 1975
Published: 1 January 1976
David M. Boyd