Geodesic
The estimates of the approximation numbers of the Hardy operator acting in the Lorenz spaces in the case $\max(r,s)\leq q$
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 1, pp. 71-88

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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. 
@article{DVMG_2021_21_1_a6,
     author = {E. N. Lomakina and M. G. Nasyrova and V. V. Nasyrov},
     title = {The estimates of the approximation numbers of the {Hardy} operator acting in the {Lorenz} spaces in the case $\max(r,s)\leq q$},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_1_a6/}
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E. N. Lomakina; M. G. Nasyrova; V. V. Nasyrov. The estimates of the approximation numbers of the Hardy operator acting in the Lorenz spaces in the case $\max(r,s)\leq q$. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 1, pp. 71-88. http://geodesic.mathdoc.fr/item/DVMG_2021_21_1_a6/