Solid hulls of quasi-Banach spaces of analytic functions and interpolation

Abstract

Abstract We study solid hulls of abstract Hardy spaces of analytic functions on the unit disk. Interpolation of sublinear operators is used to description of solid hulls of quasi-Banach spaces generated by interpolation methods associated to classical Hardy spaces H p for 0 p 1 . We specialize our results to solid hulls of Hardy–Orlicz and Hardy–Lorentz spaces and we are able to characterize multipliers from Hardy–Lorentz spaces to any solid sequence space. We give, for example, a complete description of multipliers with the domain in Hardy–Lorentz–Zygmund spaces.