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   <subfield code="a">Littlewood-Paley operators defined on a new kind of generalized Lipschitz spaces ɛ 0 α,p 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 ɛ 0 α,p , where −n&lt;α&lt;1 and 1&lt;p&lt;∞.</subfield>
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