Geodesic
Volterra type integral operators with homogeneous kernels in weighted $L_p$-spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 3-12

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We consider the multidimensional integral Volterra type operators with homogeneous of degree $(-n)$ kernels, acting in $L_p$-spaces with submultiplicative weight. For these operators we obtain the necessary and sufficient conditions of invertibility. Besides, we describe the Banach algebra generated by these operators. For this algebra we construct the symbolic calculus, in terms of which we obtain the invertibility criterion of operators.
Keywords: integral operator, homogeneous kernel, invertibility, Banach algebra, spherical harmonics.
Mots-clés : symbol 
@article{IVM_2017_11_a0,
     author = {O. G. Avsyankin},
     title = {Volterra type integral operators with homogeneous kernels in weighted $L_p$-spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--12},
     publisher = {mathdoc},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_11_a0/}
}
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O. G. Avsyankin. Volterra type integral operators with homogeneous kernels in weighted $L_p$-spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 3-12. http://geodesic.mathdoc.fr/item/IVM_2017_11_a0/