Multipliers on weighted Hardy spaces over locally compact Vilenkin groups

A weighted H-omega(p)(G) multiplier theorem on the multiplier operator T as sociated with a function m is an element of L-infinity(Gamma) is shown and the atomic decomposition of functions f in H-omega(p)(G) is obtained, where G is a Vilenkin group, Gamma its dual, 0 < p less than or equal to 1 and o mega is a weight on G which is more general than that proposed by C. W. Onn eweer et al.