Function Spaces Determined by A Levelling Length Function
- 1 January 1953
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 5, 576-592
- https://doi.org/10.4153/cjm-1953-065-1
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.)Keywords
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