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 Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by Sawyer estimating the $L^{1,\infty }(uv)$ norm of $v^{-1}T(fv)$ for special cases. The emphasis is made in proving new and more precise quantitative estimates involving the $A_p$ or $A_{\infty }$ constants of the weights involved.

typos added, reorganized the introduction. To appear in Indiana Math. Journal