On weighted strong type inequalities for the generalized weighted mean operator

摘要

The generalized weighted mean operator M~g _w is given by where w is a positive measurable function on (0, + ∞) and g is a real continuous strictly monotone function with its inverse g~(-1). We give some sufficient conditions on weights u, v on (0, + ∞) for which there exists a positive constant C such that the weighted strong type (p, q) inequality holds for every measurable non-negative function f, where the positive reals p,q satisfy certain restrictions.