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Vladikavkazskii Matematicheskii Zhurnal, 2014, Volume 16, Number 1, Pages 12–23
(Mi vmj491)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/vmj491 https://www.mathnet.ru/eng/vmj/v16/i1/p12
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Abstract page: | 265 | Full-text PDF : | 80 | References: | 66 |
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