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

DOI

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
@article{10_4153_CMB_2002_003_x,
     author = {Bloom, Steven and Kerman, Ron},
     title = {Extrapolation of {Lp} {Data} from a {Modular} {Inequality}},
     journal = {Canadian mathematical bulletin},
     pages = {25--35},
     year = {2002},
     volume = {45},
     number = {1},
     doi = {10.4153/CMB-2002-003-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-003-x/}
}
TY  - JOUR
AU  - Bloom, Steven
AU  - Kerman, Ron
TI  - Extrapolation of Lp Data from a Modular Inequality
JO  - Canadian mathematical bulletin
PY  - 2002
SP  - 25
EP  - 35
VL  - 45
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-003-x/
DO  - 10.4153/CMB-2002-003-x
ID  - 10_4153_CMB_2002_003_x
ER  - 
%0 Journal Article
%A Bloom, Steven
%A Kerman, Ron
%T Extrapolation of Lp Data from a Modular Inequality
%J Canadian mathematical bulletin
%D 2002
%P 25-35
%V 45
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-003-x/
%R 10.4153/CMB-2002-003-x
%F 10_4153_CMB_2002_003_x

Cité par Sources :