Geodesic
Alternative characterisations of Lorentz-Karamata spaces
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 517-540.

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We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
Classification : 26D10, 42B35, 46E30, 47B38, 47G10
Keywords: Lorentz-Karamata spaces; equivalent quasi-norms; weighted norm inequalities; fractional maximal operators; Riesz potentials 
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     title = {Alternative characterisations of {Lorentz-Karamata} spaces},
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Edmunds, D. E.; Opic, B. Alternative characterisations of Lorentz-Karamata spaces. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 517-540. http://geodesic.mathdoc.fr/item/CMJ_2008__58_2_a16/