On estimates for the norms of the Hardy operator acting in the Lorenz spaces

E. N. Lomakina

Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 2, pp. 191-211

Résumé

In the paper conditions are found under which the compact operator $Tf(x)=\varphi(x)\int_0^xf(\tau)v(\tau)\,d\tau,$ $x>0,$ acting in weighted Lorentz spaces $T:L^{r,s}_{v}(\mathbb{R^+})\to L^{p,q}_{\omega}(\mathbb{R^+})$ in the domain $1\max (r,s)\le \min(p,q)\infty,$ belongs to operator ideals $\mathfrak{S}^{(a)}_\alpha$ and $\mathfrak{E}_\alpha$, $0\alpha\infty$. And estimates are also obtained for the quasinorms of operator ideals in terms of integral expressions which depend on operator weight functions.