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Vladikavkazskii Matematicheskii Zhurnal, 2014, Volume 16, Number 1, Pages 12–23 (Mi vmj491)  

Estimates for some potential type operators whose kernels have singularities on spheres

M. N. Gurovab, V. A. Noginba

a Southern Federal University, Rostov-on-Don, Russia
b South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
References:
Abstract: Multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in $\mathbb R^n$ are studied on Hardy spaces $H^p$, $0<p<\infty$. Necessary and sufficient conditions are obtained for such operators to be bounded from $H^p$ into the Holder space $\Lambda_s$, from $H^p$ into the Sobolev space $L_k^\infty$, and from BMO into $\Lambda_s$.
Key words: potential, Hardy spaces, space of Hölder functions, bounded mean oscillation.
Received: 17.02.2013
Document Type: Article
UDC: 517.983.2
Language: Russian
Citation: M. N. Gurov, V. A. Nogin, “Estimates for some potential type operators whose kernels have singularities on spheres”, Vladikavkaz. Mat. Zh., 16:1 (2014), 12–23
Citation in format AMSBIB
\Bibitem{GurNog14}
\by M.~N.~Gurov, V.~A.~Nogin
\paper Estimates for some potential type operators whose kernels have singularities on spheres
\jour Vladikavkaz. Mat. Zh.
\yr 2014
\vol 16
\issue 1
\pages 12--23
\mathnet{http://mi.mathnet.ru/vmj491}
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