Paper Title:

Inequalities Involving A_∞ Weights by Extrapolations

Author(s):

Chunping Xie

Mathematics Department,
Milwaukee School of Engineering,
1025 N. Broadway,
Milwaukee, Wisconsin 53202,
U.S.A.
E-mail: xie@msoe.edu
URL: https://www.msoe.edu/directory/profile/chunping.xie/

Abstract:

We generalize the extrapolation theorem from A_p weights to A_∞ weights on the setting of weighted Morrey spaces by using the Rubio de Francia algorithm and ideas in a paper by D. Cruz-Uribe et al. First we have proved the classical Hardy-Littlewood maximal operator is bounded on the weighted Morrey spaces if the weight w(x) is in A_∞ and then we have obtained inequalities involving the maximal operator, vector-valued maximal operator, the sharp maximal operator, and A_∞ weights.

Full Text PDF: