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Contents of PMS, Vol. 38, Fasc. 2,
pages 459 - 479
 

BELLMAN FUNCTIONS AND Lp ESTIMATES FOR PARAPRODUCTS

Vjekoslav Kovač
Kristina Ana Škreb

Abstract: We give an explicit formula for one possible Bellman function associated with the Lp 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 Bańuelos and Bennett and the paraproducts with respect to the heat flows.

2010 AMS Mathematics Subject Classification: Primary: 60G46; Secondary: 42B15.

Keywords and phrases: Bellman function, martingale, paraproduct.

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