# Article

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Keywords:
one-sided weights; one-sided reverse Hölder; factorization
Summary:
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.
References:
[1] H. Aimar, L. Forzani and F. J. Martín-Reyes: On weighted inequalities for one-sided singular integrals. Proc. Amer. Math. Soc. 125 (1997), 2057–2064. DOI 10.1090/S0002-9939-97-03787-8 | MR 1376747
[2] D. Cruz-Uribe and C. J. Neugebauer: The structure of reverse Hölder classes. Trans. Amer. Math. Soc. 347 (1995), 2941–2960. MR 1308005
[3] 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
[4] 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
[5] F. J. Martín-Reyes: New proofs of weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Proc. Amer. Math. Soc. 117, 691–698. DOI 10.1090/S0002-9939-1993-1111435-2 | MR 1111435
[6] F. J. Martín-Reyes, P. Ortega and A. de la Torre: Weighted inequalities for one-sided maximal functions. Trans. Amer. Math. Soc. 319 (2) (1990), 517–534. DOI 10.1090/S0002-9947-1990-0986694-9 | MR 0986694
[7] F. J. Martín-Reyes, L. Pick and A. de la Torre: $A^+_\infty$ condition. Canad. J. Math. 45 (6) (1993), 1231–1244. MR 1247544
[8] C. J. Neugebauer: The precise range of indices for the $RH_r$ and $A_p$ weight classes. Preprint (), .
[9] E. Sawyer: Weighted inequalities for the one-sided Hardy-Littlewood maximal function. Trans. Amer. Math. Soc. 297 (1986), 53–61. DOI 10.1090/S0002-9947-1986-0849466-0 | MR 0849466

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