Potential inequality
Copyright policy )Potential inequality
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.
- University of Zagreb Croatia
- University of Florida United States
Integral, integro-differential, and pseudodifferential operators, weighted inequalities, Higher-dimensional potential theory, potential type kernel, maximum principle, maximum principle; Hardy's inequality
Integral, integro-differential, and pseudodifferential operators, weighted inequalities, Higher-dimensional potential theory, potential type kernel, maximum principle, maximum principle; Hardy's inequality
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