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2002/2003 On the non-compactness of maximal operators.
G. G. Oniani
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Real Anal. Exchange 28(2): 439-446 (2002/2003).


It is proved that if \(B\) is a convex quasi-density basis and \(E\) is a symmetric space on \(\mathbb{R}^n\) with respect to Lebesgue measure, then there do not exist non-orthogonal weights \(w\) and \(v\) for which the maximal operator \(M_B\) corresponding to \(B\) acts compactly from the weight space \(E_w\) to the weight space \(E_v\).


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G. G. Oniani. "On the non-compactness of maximal operators.." Real Anal. Exchange 28 (2) 439 - 446, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1080.42506
MathSciNet: MR2009765

Primary: ‎28A15 , 42B25 , 46E30

Keywords: compactness , Maximal operator , Symmetric space

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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