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.
Keywords: one-sided integral operators, operators with homogeneous kernels, the grand Lebesgue spaces, two-sided estimates, spherical means
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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