Abstract
For a nonempty setE of nonnegative integers letH p, q, a E andH p E be the closed linear span of
in the mixed norm spaceH p, q, a E (B n ) and in the Hardy spaceH p(B n ), respectively. In this note we prove that the Hahn-Banach Extension Property (HBEP) ofH p, q, a E is independent ofq. As an application, we show that if 0<p<1 andH p, q, a E orH p E has HBEP thenE must be thick in the sense that ifE={mn∶n=1, 2,...}, wherem 1<m 2<..., thenm n<-c n for some constantc. This result is an extension over those obtained in [2] and [4].
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Jevtić, M., Pavlović, M. On the Hahn-Banach Extension Property in Hardy and mixed norm spaces on the unit ball. Monatshefte für Mathematik 111, 137–145 (1991). https://doi.org/10.1007/BF01332352
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DOI: https://doi.org/10.1007/BF01332352