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DOI: 10.23671/VNC.2017.3.7132

One-Sided Integral Operators with Homogeneous Kernels in grand Lebesgue Spaces

Umarkhadzhiev, S. M.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 3.
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.
Keywords: one-sided integral operators, operators with homogeneous kernels, the grand Lebesgue spaces, two-sided estimates, spherical means
Language: Russian Download the full text  
For citation: Umarkhadzhiev S. M. One-sided integral operators with homogeneous kernels in grand Lebesgue spaces // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 70-82. DOI 10.23671/VNC.2017.3.7132
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