one-sided weights; one-sided reverse Hölder; factorization
In this paper we study the relationship between one-sided reverse Hölder classes $RH_r^+$ and the $A_p^+$ classes. We find the best possible range of $RH_r^+$ to which an $A_1^+$ weight belongs, in terms of the $A_1^+$ constant. Conversely, we also find the best range of $A_p^+$ to which a $RH_\infty ^+$ weight belongs, in terms of the $RH_\infty ^+$ constant. Similar problems for $A_p^+$, $1<p<\infty $ and $RH_r^+$, $1<r<\infty $ are solved using factorization.
 D. Cruz-Uribe and C. J. Neugebauer: The structure of reverse Hölder classes
. Trans. Amer. Math. Soc. 347 (1995), 2941–2960. MR 1308005
 D. Cruz-Uribe, C. J. Neugebauer and V. Olesen: The one-sided minimal operator and the one-sided reverse Hölder inequality
. Stud. Math 116 (1995), 255–270. MR 1360706
 P. Guan and E. Sawyer: Regularity estimates for oblique derivative problem
. Anal. of Mathematics, Second Series 157 (1) (1993), 1–70. DOI 10.2307/2946618
| MR 1200076
 F. J. Martín-Reyes, L. Pick and A. de la Torre: $A^+_\infty $ condition
. Canad. J. Math. 45 (6) (1993), 1231–1244. MR 1247544
 C. J. Neugebauer: The precise range of indices for the $RH_r$ and $A_p$ weight classes. Preprint (), .