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One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
S. M. Umarkhadzhievab a Complex Research Institute named after Kh. I. Ibragimov, Russian Academy of Sciences, Groznyi
b Academy of Sciences of Chechen Republic
Abstract:
Sufficient conditions and necessary conditions for the kernel and the grandiser are obtained under which one-sided integral operators with homogeneous kernels are bounded in the grand Lebesgue spaces on $\mathbb{R}$ and $\mathbb{R}^n$. Two-sided estimates for grand norms of these operators are also obtained. In addition, in the case of a radial kernel, we obtain two-sided estimates for the norms of multidimensional operators in terms of spherical means and show that this result is stronger than the inequalities for norms of operators with a nonradial kernel.
Key words:
one-sided integral operators, operators with homogeneous kernels, the grand Lebesgue spaces, two-sided estimates, spherical means.
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UDC:
517.982, 517.983 Received: 20.01.2017
Citation:
S. M. Umarkhadzhiev, “One-sided integral operators with homogeneous kernels in grand Lebesgue spaces”, Vladikavkaz. Mat. Zh., 19:3 (2017), 70–82
Citation in format AMSBIB
\Bibitem{Uma17}
\by S.~M.~Umarkhadzhiev
\paper One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 3
\pages 70--82
\mathnet{http://mi.mathnet.ru/vmj626}
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http://mi.mathnet.ru/eng/vmj626 http://mi.mathnet.ru/eng/vmj/v19/i3/p70
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