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The Cameron-Storvick function space integral: An L(Lp , Lp′ ) theory

Published online by Cambridge University Press:  22 January 2016

G. W. Johnson
Affiliation:
University of Nebraska
D. L. Skoug
Affiliation:
University of Nebraska
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Extract

In [3] Cameron and Storvick introduced a very general operator-valued function space “integral”. In [3-5, 8, 9, 11, 13-20] the existence of this integral as an operator from L2 to L2 was established for certain functions. Recently the existence of the integral as an operator from L1 to L, has been studied [6, 7, 21]. In this paper we study the integral as an operator from Lp to Lp′, where 1 < p ≤ 2. The resulting theorems extend the theory substantially and indicate relationships between the L2-L2 and L1-L theories that were not apparent earlier. Even in the most studied case, p = p′ = 2, the results below strengthen the theory.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

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