Real Analysis Exchange

On the non-compactness of maximal operators.

G. G. Oniani

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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

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

First available in Project Euclid: 20 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

maximal operator compactness symmetric space


Oniani, G. G. On the non-compactness of maximal operators. Real Anal. Exchange 28 (2002), no. 2, 439--446.

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