Some Measurability Results and Applications to Spaces with Mixed Family-norm

Some Measurability Results and Applications to Spaces with Mixed Family-norm A space with mixed family-norm consists of all functions x on a product space such that the function [InlineMediaObject not available: see fulltext.] belongs to V (here, U(t) and V denote given Köthe spaces). Conditions for the measurability of y are given, and the Köthe dual of such spaces is determined. For this purpose a generalization of the Luxemburg-Gribanov theorem for ‘uniformly measurable’ functions is proved. This result is also formulated for vector functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Some Measurability Results and Applications to Spaces with Mixed Family-norm

Positivity , Volume 10 (4) – Jul 11, 2006

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-005-0035-9
Publisher site
See Article on Publisher Site

Abstract

A space with mixed family-norm consists of all functions x on a product space such that the function [InlineMediaObject not available: see fulltext.] belongs to V (here, U(t) and V denote given Köthe spaces). Conditions for the measurability of y are given, and the Köthe dual of such spaces is determined. For this purpose a generalization of the Luxemburg-Gribanov theorem for ‘uniformly measurable’ functions is proved. This result is also formulated for vector functions.

Journal

PositivitySpringer Journals

Published: Jul 11, 2006

References

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