| Title:
|
On the best ranges for $A^+_p$ and $RH_r^+$ (English) |
| Author:
|
Riveros, M. S. |
| Author:
|
Torre, A. de la |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
285-301 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
one-sided weights |
| Keyword:
|
one-sided reverse Hölder |
| Keyword:
|
factorization |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 0980.42015 |
| idMR:
|
MR1844311 |
| . |
| Date available:
|
2009-09-24T10:42:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127648 |
| . |
| Reference:
|
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| Reference:
|
[2] D. Cruz-Uribe and C. J. Neugebauer: The structure of reverse Hölder classes.Trans. Amer. Math. Soc. 347 (1995), 2941–2960. MR 1308005 |
| Reference:
|
[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, 10.4064/sm-116-3-255-270 |
| Reference:
|
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| Reference:
|
[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. MR 1111435, 10.1090/S0002-9939-1993-1111435-2 |
| Reference:
|
[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. MR 0986694, 10.1090/S0002-9947-1990-0986694-9 |
| Reference:
|
[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 |
| Reference:
|
[8] C. J. Neugebauer: The precise range of indices for the $RH_r$ and $A_p$ weight classes.Preprint (), . |
| Reference:
|
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| . |
