Bellman functions and $L^p$ estimates for paraproducts

Kristina Ana \v{S}kreb; Vjekoslav Kova\v{c}

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Bellman functions and $L^p$ estimates for paraproducts

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arxiv 1609.02895 v3 pith:BTVAYJC2 submitted 2016-09-09 math.PR math.CA

Vjekoslav Kovač , Kristina Ana Škreb This is my paper

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keywords paraproductsbellmanestimatesfunctiongiveoperatorsalternativeapply

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abstract

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.

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