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.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 65, pp. 5–16, 1976.
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Bukhvalov, A.V. Hardy spaces of vector-valued functions. J Math Sci 16, 1051–1059 (1981). https://doi.org/10.1007/BF02427716
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DOI: https://doi.org/10.1007/BF02427716