Sharp off-diagonal weighted weak type estimates for sparse operators

2018/04/20 by Qianjun He, He, Qianjun, Dunyan Yan +1
Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1804.08447

Abstract

We prove sharp weak type weighted estimates for a class of sparse operators that includes majorants of standard α-fractional singular integrals, fractional integral operators, Marcinkiewicz integral operators, and square functions. These bounds are knows to be sharp in many cases, and our main new result is the optimal bound [w]_A_p,q^(1)/(q)[w^q]_A_∞^{(1)/(2)-(1)/(p)}\lesssim[w]_A_p,q^(1)/(2)-\fracαd for proper conditions which satisfy that three index p, q and α ensure weak type norm of fractional square functions on L^q(w^q) with p>2.

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