Potential inequality |
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| Authors: | Murali Rao Hrvoje Šikić |
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| Institution: | (1) Department of Mathematics, University of Florida, 32611 Gainesville, FL, USA;(2) Department of Mathematics, University of Florida, 32611 Gainesville, FL, USA;(3) Department of Mathematics, University of Zagreb, 41000 Zagreb, Croatia |
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| Abstract: | We prove a general inequality for kernels satisfying the maximum principle. This is then used to derive a sufficient condition
for the kernel to define a continuous map of Lebesgue spaces. Exactly this condition happens to be necessary and sufficient
for the validity of Hardy’s inequality with weights in one dimension. Some applications indicating the unifying nature of
the potential inequality are given.
A part of this paper was presented at the 865th AMS meeting, March 1991, Tampa, Florida. |
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