Geodesic
Reverse-Holder classes in the Orlicz spaces setting
Studia Mathematica, Tome 130 (1998) no. 3, pp. 245-261

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In connection with the $A_ϕ $ classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes $RH_ϕ$. We prove that when ϕ is $Δ_2$ and has lower index greater than one, the class $RH_ϕ$ coincides with some reverse-Hölder class $RH_q,q>1$. For more general ϕ we still get $RH_ϕ ⊂ A_∞ = ⋃_{q>1}RH_q$ although the intersection of all these $RH_ϕ$ gives a proper subset of $⋂_{q>1}RH_q$.
DOI : 10.4064/sm-130-3-245-261
Keywords: reverse-Hölder class, $A_p$ classes of Muckenhoupt, Orlicz spaces

E. Harboure 1 ; O. Salinas 1 ; B. Viviani 1

1 
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E. Harboure; O. Salinas; B.  Viviani. Reverse-Holder classes in the Orlicz spaces setting. Studia Mathematica, Tome 130 (1998) no. 3, pp. 245-261. doi: 10.4064/sm-130-3-245-261

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