Geodesic
One-sided integral operators with homogeneous kernels in grand Lebesgue spaces
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 70-82

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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. 
@article{VMJ_2017_19_3_a7,
     author = {S. M. Umarkhadzhiev},
     title = {One-sided integral operators with homogeneous kernels in grand {Lebesgue} spaces},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {70--82},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/}
}
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S. M. Umarkhadzhiev. One-sided integral operators with homogeneous kernels in grand Lebesgue spaces. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 70-82. http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a7/