2007/10/26 by Hartmann, Andreas · 1 citation
#30E05 #30H05 #46E30 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.0710.5066
We study multipliers of Hardy-Orlicz spaces \mHΦ which are strictly contained between \bigcupp>0Hp 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 Hp, the multipliers reduce to H∞. For Hardy-Orlicz spaces \mHΦ 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 Φ. Even if the results do not entirely characterize the multiplier algebra, some examples show that we are not very far from precise conditions. In certain situations we see how the multiplier algebra grows in a sense from \Hi to big Hardy-Orlicz spaces when we go from classical Hp 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 \Hi 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 \bigcupp>0Hp 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 Hp, p>0.