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- W2963569013 abstract "We study multipliers of Hardy-Orlicz spaces ${mathcal H}_{Phi}$ which are strictly contained between $bigcup_{p>0}H^p$ and so-called big Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{infty}$. For Hardy-Orlicz spaces ${mathcal H}_{Phi}$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $Phi$. In general it cannot be expected to obtain a characterization of the multiplier algebra in terms of Hardy-Orlicz spaces since these are in general not algebras. Nevertheless, some examples show that we are not very far from such a characterization. In certain situations we see how the multiplier algebra grows in a sense from $H^{infty}$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to big Hardy-Orlicz spaces. However, the multiplier algebras are not always ordered as their underlying Hardy-Orlicz spaces. Such an ordering holds in certain situations, but examples show that there are large Hardy-Orlicz spaces for which the multipliers reduce to $H^{infty}$ so that the multipliers do in general not conserve the ordering of the underlying Hardy-Orlicz spaces. We apply some of the multiplier results to construct Hardy-Orlicz spaces close to $bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longer characterized by the Carleson condition which is well known to characterize free interpolating sequences in $H^p$, $p>0$." @default.
- W2963569013 created "2019-07-30" @default.
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- W2963569013 date "2010-03-01" @default.
- W2963569013 modified "2023-10-18" @default.
- W2963569013 title "Pointwise multipliers in Hardy-Orlicz spaces, and interpolation" @default.
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- W2963569013 doi "https://doi.org/10.7146/math.scand.a-15128" @default.
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