Abstract
In this paper Hardy inequalities are proved between weighted LP, L9 spaces with indices p, q less than 1. The results are almost characterizations of those weights for which weighted estimates hold. In this note we prove weighted Hardy inequalities with mixed indices less than 1. The results are almost characterizations of those weights for which weighted estimates hold. Our theorems correspond closely to the characterizations given by Bradley [2] (and independently by Andersen and Muckenhoupt) for indices p, q with I 1. Furthermore, they complement and extend some of those recently given in [4]. Let u, v and f denote nonnegative extended real valued measurable functions on (0, ox). Forr > 0 andp, q < ,p #0, q # 0, we define KandJ by K(r) r(r(X) dx) (lo V(x) P dx)I/
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