Sharp constants related to the triangle inequality in Lorentz spaces

Sorina Barza, Viktor Kolyada, Javier Soria

We study the Lorentz spaces $L^{p,s}(R,\mu )$ in the range $1<p<s\le \infty$, for which the standard functional $$||f|{|}_{p,s}=({\int }_0^{\infty }(t^{1/p}{f}^{\ast }(t){)}^s\frac{dt}{t}{)}^{1/s}$$ i…