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Littlewood-Paley operators defined on a new kind of generalized Lipschitz spaces E α,p 0 are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in E α,p 0 , where −n < α < 1 and 1 < p < ∞. 1991 Mathematics Subject Classification. 42B25.doi:10.1007/bf02256799 fatcat:2ouowydkivchpbvp3ussd6fqcq