Capacitary inequalities for energy (Q1112982)

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scientific article; zbMATH DE number 4079854
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Capacitary inequalities for energy
scientific article; zbMATH DE number 4079854

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    Capacitary inequalities for energy (English)
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    1988
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    The following strong capacitary inequality is obtained: \[ \int^{\infty}_{0}tc(s>t)dt\leq const.\| s\|^ 2_ e. \] Where s is an excessive function of finite energy. As Prof. Meyer observed this is a simple consequence of Doob's inequality. However the proof given uses only the (weak) maximum principle and so the result holds for kernels such as M. Riesz kernels which are not necessarily potential kernels.
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    capacitary inequality
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    excessive function
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    finite energy
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    Doob's inequality
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    maximum principle
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    Riesz kernels
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