Geodesic
Extrapolation of Lp Data from a Modular Inequality
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 25-35

Voir la notice de l'article provenant de la source Cambridge University Press

If an operator $T$ satisfies a modular inequality on a rearrangement invariant space ${{L}^{\rho}}\left( \Omega ,\mu\right)$ , and if $p$ is strictly between the indices of the space, then the Lebesgue inequality $\int{|Tf{{|}^{P}}\le C\int{|f{{|}^{P}}}}$ holds. This extrapolation result is a partial converse to the usual interpolation results. A modular inequality for Orlicz spaces takes the form $\int{\Phi \left( |Tf| \right)\le }\int{\Phi \left( C|f| \right)}$ , and here, one can extrapolate to the (finite) indices $i\left( \Phi\right)$ and $I\left( \Phi\right)$ as well.
DOI : 10.4153/CMB-2002-003-x
Mots-clés : 42B25 
Bloom, Steven; Kerman, Ron. Extrapolation of Lp Data from a Modular Inequality. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 25-35. doi: 10.4153/CMB-2002-003-x
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