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We give a generalized form of the Hormander-Schwartz-Triebel theorem for singular integral operators of potential type as well as a sequentiaI version. Applications include fractionary maximal inequalities of Hardy- Littlewood and Fefferman-Stein type.

Abstract. Partitions of the sphere S n and of the real projective space P n (R) are constructed and are applied to study inequalities on weighted Orlicz spaces for a vector-valued extension of the Hardy-Littlewood maximal operator for functions with values in an UMD Banach space. (2000): 42B25. Mathematics subject classification