Abstract: | The purpose of this paper is to consider the relations among the various definitions of the spaces Hp of analytic functions with values in a Banach space and to investigate the problem of the structure of the conjugates of
these spaces. In particular, one constructs an example of a reflexive separable Banach space χ, for which the equality Hp(X)*=Hp′(X*) (1<p<∞,1/p+1/p′=1) ails.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 65, pp. 5–16, 1976. |