REPRESENSIBILITY OF CONES OF MONOTONE FUNCTIONS IN WEIGHTED LEBESGUE SPACES AND EXTRAPOLATION OF OPERATORS ON THESE CONES

摘要

It is shown that a sublinear operator is bounded on the cone of monotone functions if and only if a certain new operator related to the one mentioned above is bounded on a certain ideal space defined constructively. This construction is used to provide new extrapolation theorems for operators on the cone in weighted Lebesgue spaces.