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Let G be a locally compact Vilenkin group with dual group 0. We prove Littlewood-Paley type inequalities corresponding to arbitrary coset decompositions of 0. These inequalities are then applied to obtain new L p .G/ multiplier theorems. The sharpness of some of these results is also discussed. 1991 Mathematics subject classification (Amer. Math. Soc.): primary 43A70, 43A22.doi:10.1017/s1446788700035941 fatcat:sxnkgqukcjhlfjpvx7lgy3trwm