WEAK AND STRONG A(p)-A(infinity) ESTIMATES FOR SQUARE FUNCTIONS AND RELATED OPERATORS

摘要

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound left perpendicular w right perpendicular(Ap)(1/p) left perpendicular w right perpendicular(A infinity)(1/2) (1/p) less than or similar to left perpendicular w right perpendicular(Ap)(1/2) for the weak type norm of square functions on L-p(w) for p 2; previously, such a bound was only known with a logarithmic correction. By the same approach, we also recover several related results in a streamlined manner.