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Статья
2017

Volterra type integral operators with homogeneous kernels in weighted L p -spaces


O. G. AvsyankinO. G. Avsyankin
Русская математика
https://doi.org/10.3103/S1066369X17110019
Abstract / Full Text

We consider multidimensional integral Volterra type operators with kernels homogeneous of degree (−n); the operators act in L p -spaces with a submultiplicative weight. For these operators we obtain necessary and sufficient conditions of their invertibility. Besides, we describe the Banach algebra generated by the operators. For this algebra we construct the symbolic calculus, in terms of which we obtain an invertibility criterion of the operators.

Author information
  • Southern Federal University, ul. Mil’chakova 8a, Rostov-on-Don, 344090, RussiaO. G. Avsyankin
References
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