Off-diagonal sharp two-weight estimates for sparse operators

Abstract

For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight estimates of mixed type in the two-weight and $A_{\infty }$-characteristics. These bounds are known to be sharp in many cases; as a new result, we prove their sharpness for fractional square functions.

15 pages. V3: Intro revised and references added. Several cases of the main theorem, claimed as new in V1 and V2, were already known, as now explained in the intro. This version is published in NYJM