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Some Linear Operators in the Lp Spaces

Published online by Cambridge University Press:  20 November 2018

Lee Peng-Yee
Lee Peng-Yee*
Affiliation:
University of Auckland, Auckland, New Zealand
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Let Lp,1 ≦ p< ∞, denote the space of all functions ƒ (real or complex) such that ƒ and |ƒ|pare variationally integrable (see 2, p. 40, for definition) with respect to a pair h of interval functions in an elementary set E. In what follows, we fix both h and E and assume that h = {hl ht}is variationally integrable and hs ≧ 0 (s = l, r)in E. Further, let L∞denote the space of all functions ƒ (real or complex) which are h-measurable (cf. 2, p. 95) and bounded almost everywhere, i.e. except in a set X satisfying (cf. 2, p. 47) V(h; E; X)= 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 648 - 654
Copyright
Copyright © Canadian Mathematical Society 1969

References

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