A Muckenhoupt’s weight problem and vector valued maximal inequalities over local fields

Abstract

In this paper, an important and interesting Muckenhoupt’s problem over local fields was firstly solved. Weighted weak and strong type norm inequalities for the Fefferman-Stein vector-valued maximal operator were firstly established over local fields, too. These results are very useful. They could be applied in various mathematical areas, for instance, in theories of functions, of partial differential equations, in harmonic analysis.