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New bounds for bilinear Calder\'on-Zygmund operators and applications

Mahdi Hormozi (Institutionen för matematiska vetenskaper) ; Kangwei Li ; Wendolin Dami\'an

In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hyt\"onen, 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 Hrus\v{c}\v{e}v classical constants. These estimates have many new applications including mixed bounds for multilinear Calder\'on--Zygmund operators and their commutators with $BMO$ functions, square functions and multilinear Fourier multipliers.

Denna post skapades 2015-12-09.
CPL Pubid: 227751


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