On the BBM-phenomenon in fractional Poincar\'e-Sobolev inequalities with weights
| Autor: | Hurri-Syrjänen, Ritva, Martínez-Perales, Javier C., Pérez, Carlos, Vähäkangas, Antti V. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we unify and improve some of the results of Bourgain, Brezis and Mironescu and the weighted Poincar\'e-Sobolev estimate by Fabes, Kenig and Serapioni. More precisely, we get weighted counterparts of the Poincar\'e-Sobolev type inequality and also of the Hardy type inequality in the fractional case under some mild natural restrictions. A main feature of the results we obtain is the fact that we keep track of the behaviour of the constants involved when the fractional parameter approaches to $1$. Our main method is based on techniques coming from harmonic analysis related to the self-improving property of generalized Poincar\'e inequalities. Comment: In the first version of the paper there was an issue with inequality (1.8) since the factor $\delta^{\frac{1}{p}}$ on the right-hand side has to be omitted in the general case. This is certainly not relevant to our contribution in the paper, but in order to correct this issue and not propagate the imprecision, we decided to remove the factor $\delta^{1/p}$ from every incorrect appearance |
| Databáze: | arXiv |
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