New bounds for bilinear Calderon-Zygmund operators and applications

Journal article, 2018

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