Weighted Doubling Measures With Remotely Constant Weights

Santi Tasena, Sompong Dhompongsa

In this work, the authors define a new class of weight functions for which its associated class of weighted measures is doubling. Moreover, all weight functions of weighted doubling measures are limit functions of this class of weighted functions with uniformly bounded doubling constant. One particular implication is that all weight functions for weighted doubling measures are equivalent to semicontinuous functions.