We extend the Littlewood-Paley theorem to L-w(p)(G), where G is a locally compact Vilenkin group and w are weights satisfying the Muckenhoupt A(p) condition. As an application we obtain a mixed-norm type multiplier result on L-w(p)(C) and prove the sharpness of our result. We also obtain a sufficient condition phi is an element of L-infinity(T) to be a multiplier on the power weighted L-alpha(p)(G) in terms of its smoothness condition. (C) 1997 Academic Press. [References: 15]
展开▼
