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

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.

Two-Weight Norm Inequality and Carleson Measure in Weighted Hardy Spaces

Let (X, ν, d) be a homogeneous space and let Ω be a doubling measure on X. We study the characterization of measures μ on X+ = X x R+ such that the inequality , where q < p, holds for the maximal operator Hvf studied by Hörmander. The solution utilizes the concept of the “balayée” of the measure μ.