We consider the inequality $f \geqslant f\star f$ for real integrable functions on $d$ dimensional Euclidean space where $f\star denotes convolution of $f$ with itself. show that all such are non-negative, which is not case same in $L^p$ any $1 < p \leqslant 2$, defined. also solutions satisfy $\int f(x){\rm d}x \tfrac12$. Moreover, if = \tfrac12$, then must decay fairly slowly: |x| \infty$, an...
