Article
| Title: | On optimal parameters involved with two-weighted estimates of commutators of singular and fractional operators with Lipschitz symbols (English) |
| Author: | Pradolini, Gladis |
| Author: | Recchi, Jorgelina |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 733-754 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove two-weighted norm estimates for higher order commutator of singular integral and fractional type operators between weighted $L^p$ and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces belong to a certain region out of which the classes of weights are satisfied by trivial weights. We also exhibit pairs of nontrivial weights in the optimal region satisfying the conditions required. (English) |
| Keyword: | fractional operator |
| Keyword: | singular integral operator |
| Keyword: | commutator |
| Keyword: | weight |
| MSC: | 42B20 |
| MSC: | 42B25 |
| MSC: | 42B35 |
| idZBL: | Zbl 07729535 |
| idMR: | MR4632855 |
| DOI: | 10.21136/CMJ.2023.0222-22 |
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| Date available: | 2023-08-11T14:22:08Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151772 |
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| Reference: | [10] Pradolini, G.: A class of pairs of weights related to the boundedness of the fractional integral operator between $L^p$ and Lipschitz spaces.Commentat. Math. Univ. Carol. 42 (2001), 133-152. Zbl 1055.42015, MR 1825378 |
| Reference: | [11] Pradolini, G.: Two-weighted norm inequalities for the fractional integral operator between $L^p$ and Lipschitz spaces.Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 41 (2001), 147-169. Zbl 0997.42010, MR 1876717 |
| Reference: | [12] Pradolini, G., Ramos, W., Recchi, J.: On the optimal numerical parameters related with two weighted estimates for commutators of classical operators and extrapolation results.Collect. Math. 72 (2021), 229-259. Zbl 1457.42029, MR 4204587, 10.1007/s13348-020-00287-1 |
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