Weighted bilinear Hardy inequalities.

Abstract

We characterize the weights w, w1, w2 such that the weighted bilinear Hardy inequality b a x a f q x a g q w(x)dx 1q C b a f p1w1 1 p1 b a gp2 w2 1 p2 holds for all nonnegative functions f and g, with a positive constant C independent of f and g, for all possible values of q, p1 and p2 with 1 < q, p1, p2 <∞. We also characterize the good weights for the weighted bilinear n-dimensional Hardy inequality to hold.