Bellman functions and $L^p$ estimates for paraproducts
| Autor: | Kovač, Vjekoslav, Škreb, Kristina Ana |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Probab. Math. Statist. 38 (2018), 459-479 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.19195/0208-4147.38.2.11 |
| Popis: | We give an explicit formula for one possible Bellman function associated with the $L^p$ boundedness of dyadic paraproducts regarded as bilinear operators or trilinear forms. Then we apply the same Bellman function in various other settings, to give self-contained alternative proofs of the estimates for several classical operators. These include the martingale paraproducts of Ba\~{n}uelos and Bennett and the paraproducts with respect to the heat flows. Comment: 18 pages, 1 figure, 1 ancillary file (Mathematica notebook); v3: exposition is slightly improved, additional calculations and remarks included |
| Databáze: | arXiv |
| Externí odkaz: |
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