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This article is cited in 1 scientific paper (total in 1 paper)
Compactness criterion for fractional integration operator of infinitesimal order
A. M. Abylayeva, A. O. Baiarystanov L. N. Gumilev Eurasian National University, Astana
Abstract:
We obtain necessary and sufficient conditions of compactness for the operator
$$Kf(x)=\int\limits_{0}^{x}\ln\frac{x}{x-s}\frac{f(s)}{s}ds$$
from $L_{p,v}$ in $L_{q,u}$ at $1<p\leq q<\infty$ and
$v(x)=x^{-\gamma}$, $\gamma>0$, where $L_{q,u}$ is the set of all measurable on $(0, \infty)$ functions $f$ with finite norm $\|uf\|_{q}$.
Keywords:
compactness, fractional integration operator, Riemann–Liouville operator, singular operator, adjoint operator, Holder inequality, weighted inequalities.
Received: 23.12.2011
Citation:
A. M. Abylayeva, A. O. Baiarystanov, “Compactness criterion for fractional integration operator of infinitesimal order”, Ufa Math. J., 5:1 (2013), 3–10
Linking options:
https://www.mathnet.ru/eng/ufa182https://doi.org/10.13108/2013-5-1-3 https://www.mathnet.ru/eng/ufa/v5/i1/p3
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Abstract page: | 502 | Russian version PDF: | 189 | English version PDF: | 27 | References: | 81 | First page: | 2 |
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