New bounds for bilinear Calderón-Zygmund operators and applications

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.

35 pages, accepted for publication in Revista Matemática Iberoamericana

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