All conditions for Stein-Weiss inequalities are necessary

Quôc Anh Ngô

The famous Stein-Weiss inequality on ${\mathbf{R}}^n\times {\mathbf{R}}^n$, also known as the doubly weighted Hardy-Littlewood-Sobolev inequality, asserts that \[ \Big| \iint_{\mathbf R…