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This article is cited in 2 scientific papers (total 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. Lomakinaa, M. G. Nasyrovaa, V. V. Nasyrovb a 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.
Received: 10.03.2021
Citation:
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 $\max(r,s)\leq q$”, Dal'nevost. Mat. Zh., 21:1 (2021), 71–88
Linking options:
https://www.mathnet.ru/eng/dvmg448 https://www.mathnet.ru/eng/dvmg/v21/i1/p71
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