This article is cited in 2 papers

The estimates of the approximation numbers of the Hardy operator acting in the Lorenz spaces in the case $\max(r,s)\leq q$

E. N. Lomakina^a, M. G. Nasyrova^a, V. V. Nasyrov<sup>b

a</sup> Computer Centre of Far Eastern Branch RAS, Khabarovsk
^b Pacific National University, Khabarovsk

Abstract: 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.

Key words: Hardy operator, compact operator, Lorentz spaces, approximation numbers, entropy numbers.

UDC: 517.51

MSC: Primary 46E30; Secondary 47B38

Received: 10.03.2021

DOI: 10.47910/FEMJ202107