Weighted Lebesgue and BMOγdocumentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$BMO^gamma $$end{document} norm inequalities for the Calderón and Hilbert operators

摘要

Necessary and sufficient conditions are given for generalized Calderón and Hilbert operators to be bounded from weighted Lebesgue spaces into suitable weighted BMO and Lipschitz spaces. Moreover, we have obtained new results on the boundedness of these operators from L∞documentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$L^{infty }$$end{document} into BMO, even in the unweighted case for the Hilbert operator. The class of weights involved are close to the doubling and reverse H?lder conditions related to the Muckenhoupt’s classes.