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Mikhlin’s problem on Carnot groups

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Abstract

We consider one class of singular integral operators over the functions on domains of Carnot groups. We prove the L p boundedness, 1 < p > ∞, for the operators of this class. Similar operators over the functions on domains of Euclidean space were considered by Mikhlin.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    N. N. Romanovskii

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  1. N. N. Romanovskii
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Correspondence to N. N. Romanovskii.

Additional information

Original Russian Text Copyright © 2008 Romanovskiĭ N. N.

The author was supported by the Russian Foundation for Basic Research (Grant 06-01-00735-a), a grant of the President of the Russian Federation for Young Science Doctors, the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-8526.2006.1), and the Lavrent’ev Young Scientists Competition (No. 5).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 1, pp. 193–206, January–February, 2008.

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Romanovskii, N.N. Mikhlin’s problem on Carnot groups. Sib Math J 49, 155–165 (2008). https://doi.org/10.1007/s11202-008-0016-x

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  • DOI: https://doi.org/10.1007/s11202-008-0016-x

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