Two-Weight Norm Inequality for the One-Sided Hardy-Littlewood Maximal Operators in Variable Lebesgue Spaces

Abstract

The authors establish the two-weight norm inequalities for the one-sided Hardy-Littlewood maximal operators in variable Lebesgue spaces. As application, they obtain the two-weight norm inequalities of variable Riemann-Liouville operator and variable Weyl operator in variable Lebesgue spaces on bounded intervals.

Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions

“…[6,Chapter 12,p.338 ], [10], [35]), Uryson type operators (see e.g [6, Chapter 12, p.339 ], [16]) and Hardy-Littlewood type operators (see e.g. [9], [17], [26], [31]).…”