Real Analysis Exchange

On the non-compactness of maximal operators.

G. G. Oniani

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Abstract

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 \(E_v\).

Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 439-446.

Dates
First available in Project Euclid: 20 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.rae/1184963806

Mathematical Reviews number (MathSciNet)
MR2009765

Zentralblatt MATH identifier
1080.42506

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 28A15: Abstract differentiation theory, differentiation of set functions [See also 26A24]

Keywords
maximal operator compactness symmetric space

Citation

Oniani, G. G. On the non-compactness of maximal operators. Real Anal. Exchange 28 (2002), no. 2, 439--446. https://projecteuclid.org/euclid.rae/1184963806


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References

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  • G. Oniani, On the integrability of strong maximal functions corresponding to different frames, Georgian Math. J., 6 (1999), 149–168.