I think the following inequality is correct. While I cannot prove it rigorously. Would someone help me to prove it? Thanks very much!
$$ \iint_{\{|y|\le R\}} \frac{1}{|x-y|^{n-1}} dy \le \iint_{\{|y|\le R\}} \frac{1}{|y|^{n-1}} dy $$ for any $x$ such that $|x|<R$.