A Characterization of Lp among Rearrangement Invariant Function Spaces

A Characterization of Lp among Rearrangement Invariant Function Spaces Positivity 4: 253–258, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. A Characterization of L among Rearrangement Invariant Function Spaces 1;? 2;† FRANCISCO L. HERNANDEZ and EVGUENI M. SEMENOV Dpto. Analisis Matematico, Facultad de Matematicas, Universidad Complutense, 28040-Madrid, Spain E-mail: pacoh@eucmax.sim.ucm.es Dept. of Mathematics, Voronez State University, 394693-Voronez, Russia E-mail: root@func.vsu.su Supported by DGICYT (Spain), grant PB97-0240. Supported by RFFI (Russia), grant 98-01-00044 and Universities of Russia grant. Dedicated to the memory of Charles B. Huijsmans. In this note we are interested on the complementability of sublattices of rearrange- ment invariant (r.i.) Banach function spaces ET0;1/ D E generated by sequences of disjoint equimeasurable functions onT0;1/. Given a function a in ET0; 1/,we consider the sequence .a / defined by the translations of a.t/ on the Tk 1;k/ interval, and its closed span Ta UD Q . We study the complementability of the k a sublattices Q in E. An r.i. Banach function space E is said to be nice if every sublattice of type Q is a complemented subspace for any function a 2 ET0; 1/. We present a characterization of L -spaces, 1 <p < 1, among the class of r.i. Banach function spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

A Characterization of Lp among Rearrangement Invariant Function Spaces

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Kluwer Academic Publishers
Copyright © 2000 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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