L^p estimates for a singular integral operator motivated by Calderón's second commutator

Details L^p estimates for a singular integral operator motivated by Calderón's second commutator L^p estimates for a singular integral operator motivated by Calderón's second commutator

2011-04-27

arxiv.org/abs/1104.5160v3

Mathematics

Classical Analysis and ODEs

29 pages; corrected typos

Scientific paper

We prove a wide range of L^p estimates for a trilinear singular integral operator motivated by dropping one average in Calder\'{o}n's second commutator. For comparison by dropping two averages in Calder\'{o}n's second commutator one faces the trilinear Hilbert transform. The novelty in this paper is that in order to avoid difficulty of the level of the trilinear Hilbert transform, we choose to view the symbol of the operator as a non-standard symbol. The methods used come from time-frequency analysis but must be adapted to the fact that our symbol is non-standard.

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