Function Spaces Determined by A Levelling Length Function

Abstract

In this paper we introduce the function spaces Lx and Lx(5) which generalize the classical L p and L p (B) spaces respectively. For those λ which possess what we call the levelling property we give a discussion of the conjugate space to L λ (B); our treatment applies, in particular, to the L (W) p (B) and M (W) q (B) spaces defined in [7, §2]. ( See also the note at end of this paper. )