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arXiv · 1512.02400

New bounds for bilinear Calderón-Zygmund operators and applications

Wendolín Damián·Mahdi Hormozi·Kangwei Li
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Abstract

In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calderón--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hytönen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_{\infty}$ constants inspired in the Fujii-Wilson and Hrusčěv classical constants. These estimates have many new applications including mixed bounds for multilinear Calderón--Zygmund operators and their commutators with $BMO$ functions, square functions and multilinear Fourier multipliers.

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Wendolín Damián, Mahdi Hormozi, Kangwei Li. 2016-11-27. New bounds for bilinear Calderón-Zygmund operators and applications. https://doi.org/10.4171/rmi%2F1021

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