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Partitions of the sphere Sn and of the real projective space Pn(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. Mathematics subject classification (2000): 42B25.

An inequality on weighted Orlicz spaces for a vector-valued extension of the Hardy-Littlewood maximal operator on S^n and P^n(ℝ)