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Lp Spaces from Matrix Measures: A Correction and their Interpolation

Published online by Cambridge University Press:  20 November 2018

Patrick J. Browne  and
Claude Costa
Patrick J. Browne
Affiliation:
Department of Mathematics and Statistics, The University of CalgaryCalgary, Alberta, Canada
Claude Costa
Affiliation:
Department of Mathematics and Statistics, The University of CalgaryCalgary, Alberta, Canada
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Abstract

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We discuss the construction of the spaces Lp(μij), 1 ≤ p ≤ ∞, where {μij} is an n × n positive matrix measure, correct a mistake in the literature concerning those spaces and develop an interpolation theory for them.

Keywords

46E30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 137 - 143
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Bergh, J. and Löfström, J., Interpolation Spaces, Springer-Verlag, , New York, 1976.Google Scholar
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3. Costa, C., Interpolation of Matrix Measure Function Spaces, M.Sc. Thesis, University of Calgary, 1981.Google Scholar
4. Dunford, N. and Schwartz, J. T., Linear Operators, Part II, Wiley-Interscience, New York, 1963.Google Scholar
5. Triebel, H., Interpolation Theory, Function Spaces, Differential Operators, North Holland, New York, 1978.Google Scholar