Quantitative weighted mixed weak-type inequalities for classical operators

Abstract

We improve on several mixed weak-type inequalities both for the Hardy-Littlewood maximal function and for Calder´on-Zygmund operators. These types of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating the L 1,∞(uv) norm of v −1T (f v) for special cases. The emphasis is made in proving new and more precise quantitative estimates involving the Ap or A∞ constants of the weights involved.