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Hausdorff measures and functions of bounded quadratic variation


Authors: D. Apatsidis, S. A. Argyros and V. Kanellopoulos
Journal: Trans. Amer. Math. Soc. 363 (2011), 4225-4262
MSC (2000): Primary 28A78, 46B20, 46B26
DOI: https://doi.org/10.1090/S0002-9947-2011-05209-8
Published electronically: March 15, 2011
MathSciNet review: 2792986
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Abstract | References | Similar Articles | Additional Information

Abstract: To each function $ f$ of bounded quadratic variation we associate a Hausdorff measure $ \mu_f$. We show that the map $ f\to\mu_f$ is locally Lipschitz and onto the positive cone of $ \mathcal{M}[0,1]$. We use the measures $ \{\mu_f:f\in V_2\}$ to determine the structure of the subspaces of $ V_2^0$ which either contain $ c_0$ or the square stopping time space $ S^2$.


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Additional Information

D. Apatsidis
Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
Email: dapatsidis@hotmail.com

S. A. Argyros
Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
Email: sargyros@math.ntua.gr

V. Kanellopoulos
Affiliation: Department of Mathematics, Faculty of Applied Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece
Email: bkanel@math.ntua.gr

DOI: https://doi.org/10.1090/S0002-9947-2011-05209-8
Keywords: Hausdorff measures, functions of bounded $p$-variation, Banach spaces with non-separable dual, James Function space
Received by editor(s): March 31, 2009
Received by editor(s) in revised form: July 14, 2009
Published electronically: March 15, 2011
Additional Notes: This research was supported by PEBE 2007.
Article copyright: © Copyright 2011 American Mathematical Society

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