| Title:
|
Weighted endpoint estimates for commutators of fractional integrals (English) |
| Author:
|
Cruz-Uribe, D., SFO |
| Author:
|
Fiorenza, A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
153-160 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given $\alpha $, $0<\alpha <n$, and $b\in {\mathrm BMO}$, we give sufficient conditions on weights for the commutator of the fractional integral operator, $[b,I_\alpha ]$, to satisfy weighted endpoint inequalities on $\mathbb{R}^n$ and on bounded domains. These results extend our earlier work [3], where we considered unweighted inequalities on $\mathbb{R}^n$. (English) |
| Keyword:
|
fractional integrals |
| Keyword:
|
commutators |
| Keyword:
|
BMO |
| Keyword:
|
weights |
| Keyword:
|
Orlicz spaces |
| Keyword:
|
maximal functions |
| MSC:
|
26A33 |
| MSC:
|
42B20 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 1174.42013 |
| idMR:
|
MR2309956 |
| . |
| Date available:
|
2009-09-24T11:44:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128162 |
| . |
| Reference:
|
[1] S. Chanillo: A note on commutators.Indiana Math. J. 31 (1982), 7–16. Zbl 0523.42015, MR 0642611, 10.1512/iumj.1982.31.31002 |
| Reference:
|
[2] D. Cruz-Uribe, SFO: New proofs of two-weight norm inequalities for the maximal operator.Georgian Math. J. 7 (2000), 33–42. MR 1768043, 10.1515/GMJ.2000.33 |
| Reference:
|
[3] D. Cruz-Uribe, SFO, A. Fiorenza: Endpoint estimates and weighted norm inequalities for commutators of fractional integrals.Publ. Mat. 47 (2003), 103–131. MR 1970896, 10.5565/PUBLMAT_47103_05 |
| Reference:
|
[4] J. Duoandikoetxea: Fourier Analysis. Grad. Studies Math. Vol. 29.Am. Math. Soc., Providence, 2000. MR 1800316 |
| Reference:
|
[5] J. García-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. Math. Studies Vol. 116.North Holland, Amsterdam, 1985. MR 0848136 |
| Reference:
|
[6] L. Maligranda: Orlicz spaces and interpolation.Seminars in Mathematics 5, IMECC, Universidad Estadual de Campinas, Campinas, 1989. Zbl 0874.46022, MR 2264389 |
| Reference:
|
[7] B. Muckenhoupt, R. Wheeden: Weighted norm inequalities for fractional integrals.Trans. Am. Math. Soc. 192 (1974), 261–274. MR 0340523, 10.1090/S0002-9947-1974-0340523-6 |
| Reference:
|
[8] C. Pérez: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$-spaces with different weights.Proc. London Math. Soc. 71 (1995), 135–157. MR 1327936 |
| Reference:
|
[9] C. Pérez: Endpoint estimates for commutators of singular integral operators.J. Funct. Anal. 128 (1995), 163–185. MR 1317714, 10.1006/jfan.1995.1027 |
| Reference:
|
[10] M. M. Rao, Z. D. Ren: Theory of Orlicz Spaces.Marcel Dekker, New York, 1991. MR 1113700 |
| . |
