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Abstract

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 $⋂_{q>1}RH_q$.