Mean2-Bounded Operators on Hilbert Space and Weight Sequences of Positive Operators

Mean2-Bounded Operators on Hilbert Space and Weight Sequences of Positive Operators We introduce and study the class of mean2-bounded operators on Hilbert space. These operators, which are characterized by a uniform boundedness condition on the ''quadratic averages'' of their powers, are intimately related to operator-valued weight sequences and weighted norm inequalities. Mean2-bounded operators exhibit a lively interplay with the discrete Hilbert transform in an array of settings. Under appropriate circumstances, mean2-bounded operators have a rich spectral theory leading to powerful transference properties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Mean2-Bounded Operators on Hilbert Space and Weight Sequences of Positive Operators

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1999 by Kluwer Academic Publishers
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.
10.1023/A:1009794510984
Publisher site
See Article on Publisher Site

Abstract

We introduce and study the class of mean2-bounded operators on Hilbert space. These operators, which are characterized by a uniform boundedness condition on the ''quadratic averages'' of their powers, are intimately related to operator-valued weight sequences and weighted norm inequalities. Mean2-bounded operators exhibit a lively interplay with the discrete Hilbert transform in an array of settings. Under appropriate circumstances, mean2-bounded operators have a rich spectral theory leading to powerful transference properties.

Journal

PositivitySpringer Journals

Published: Sep 28, 2004

References

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