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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 193–206 (Mi smj1833)  
This article is cited in 6 scientific papers (total in 6 papers)

Mikhlin's problem on Carnot groups

N. N. Romanovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (326 kB) Citations (6)
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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, $1<p<\infty$, for the operators of this class. Similar operators over the functions on domains of Euclidean space were considered by Mikhlin.
Keywords: Carnot group, singular integral operator, Calderón–Zygmund theorem, Mikhlin's theorem, multidimensional Fourier series.
Received: 10.07.2006
Revised: 17.04.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 1, Pages 155–165
DOI: https://doi.org/10.1007/s11202-008-0016-x
Bibliographic databases:
UDC: 517.518.13+517.518.14+512.81+517.518.475
Language: Russian
Citation: N. N. Romanovskii, “Mikhlin's problem on Carnot groups”, Sibirsk. Mat. Zh., 49:1 (2008), 193–206; Siberian Math. J., 49:1 (2008), 155–165
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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