Inequalities for $L^p$-norms that sharpen the triangle inequality and complement Hanner's Inequality

Eric A. Carlen, Rupert L. Frank, Paata Ivanisvili +1

In 2006 Carbery raised a question about an improvement on the naïve norm inequality $\Vert f+g{\Vert }_p^p\le 2^{p-1}(\Vert f{\Vert }_p^p+\Vert g{\Vert }_p^p)$ for two functions in $L^p$ of any measure spac…