Sharp inclusions and lacunary series in mixed-norm spaces on the polydisc

Abstract

We establish the sharpness and strictness of continuous inclusions in mixed-norm spaces of n-harmonic functions on the unit polydisc of ℂ n . To this end, we modify a wellknown counterexample of Hardy and Littlewood and give a characterization of lacunary series with Hadamard gaps in mixed-norm and weighted Hardy spaces.