On the Convolution Inequality <i>f ≥ f ⋆ f</i>
On the Convolution Inequality <i>f ≥ f ⋆ f</i>
We consider the inequality $f \geqslant f\star f$ for real integrable functions on $d$ dimensional Euclidean space where $f\star f$ denotes the convolution of $f$ with itself. We show that all such functions $f$ are non-negative, which is not the case for the same inequality in $L^p$ for any $1 …