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A Class of Operators on the Lorentz Space M(ϕ)

Published online by Cambridge University Press:  20 November 2018

David W. Boyd
David W. Boyd*
Affiliation:
University of Toronto
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In order to deal with certain problems in the theory of interpolation spaces, it is convenient to consider operators of the following form:

Let k be a non-negative measurable function on the half-line R+, and let ƒ be a measurable function on R+ with

1

Then the operator T is defined by

2

with the domain of T, D(T), consisting of all ƒ which satisfy (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 839 - 841
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Boyd, D. W., The Hilbert transformation in rearrangement invariant Banach spaces, Ph.D. thesis, University of Toronto, 1966.Google Scholar
2. Calderón, A. P., Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), 113–190.Google Scholar
3. Lorentz, G. G., On the theory of spaces, A, Pacific J. Math., 1 (1950), 411–429.Google Scholar