Duals and envelopes of some Hardy-Lorentz spaces

Lengfield, Marc

doi:10.1090/S0002-9939-04-07656-7

Duals and envelopes of some Hardy-Lorentz spaces
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by Marc Lengfield

Proc. Amer. Math. Soc. 133 (2005), 1401-1409

DOI: https://doi.org/10.1090/S0002-9939-04-07656-7

Published electronically: October 18, 2004

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Abstract:

For $0<p<1$ we describe the dual spaces and Banach envelopes of the spaces $H^{p,q}$ for finite values of $q$ and for $H_{0}^{p,\infty }$, the closure of the polynomials in $H^{p,\infty }$. In addition, we determine the $s$-Banach envelopes for the spaces $H^{p,q}$ in the cases $0<q<p<s\leq 1$ and $0<q<p\leq s\leq 1$.

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