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Function Spaces Determined byA Levelling Length Function

Published online by Cambridge University Press:  20 November 2018

H. W. Ellis  and
Israel Halperin
H. W. Ellis
Affiliation:
Queen's University
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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.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 576 - 592
Copyright
Copyright © Canadian Mathematical Society 1953

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