A direct and elementary proof of an estimate of Littlewood is given together with an application concerning the sharpness and strictness of some inclusions in mixed norm spaces of analytic functions.

In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces h(p, q, Î±) on the half-space are established. We prove that mixed norm isâ€¦ (More)

The paper generalizes the well-known inequality of Littlewood-Paley in the polydisc. We establish a family of inequalities which are analogues and extensions of Littlewood-Paley type inequalitiesâ€¦ (More)