We prove two-weight norm inequalities for Calderón-Zygmund singular
integrals that are sharp for the Hilbert transform and for the Riesz transforms. In addition, we give results for the dyadic square function and for commutators of singular integrals. As an application we give new results for the Sarason conjecture on the product of unbounded Toeplitz operators on Hardy spaces.Stewart Faculty Development Fund (Trinity College)Ministerio de Educación y Cienci