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 Lp and Lp(B) spaces respectively. For those λ which possess what we call the levelling property we give a discussion of the conjugate space to Lλ(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.)