Jussi Laitila, Hans-Olav Tylli, Composition Operators on Vector-valued Harmonic Functions and Cauchy Transforms, Indiana University Mathematics Journal, Vol. 55, No. 2 (2006), pp. 719-746 ...

We generalize the Hardy-Littlewood maximal functions to vector-valued functions taking values in a Banach space with a varying weight, t ↦ ρt, which satisfies a reverse Hölder condition, and prove ...