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precise evaluation – scowl certain of the rot appraise of a Newtonian potential retort

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precise evaluation – scowl certain of the rot appraise of a Newtonian potential

I’m contemplating the next Newtonian potential
$$theta(x) = int_{mathbb{R}^3}frac{1}x-yw(y) dy.$$
Here $w(y) ge 0$ is a nontrivial gentle responsibility in $L^1(mathbb{R}^3)$. Now $theta(x) ge 0$ is well-defined. Can we purchase the next appraise $$theta(x) ge frac{c}$$ for some optimistic ceaseless $c$? I arbitrator the non-negativeness of $w$ performs an needful function right here. If $w$ oscilates and adjustments enthralling often, I speculate $theta$ might rot with a charge sooner than $|x|^{-1}$.

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