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DOI: 10.23671/VNC.2014.1.7418

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

Gurov M. N. , Nogin V. A.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 1.
Abstract:
Multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in \(\Bbb{R}^n\) 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 \(\Lambda_s\).
Keywords: potential, Hardy spaces, space of Holder functions, bounded mean oscillation
Language: Russian Download the full text  
For citation: Gurov M. N., Nogin V. A. Estimates for some potential type operators whose kernels have singularities on spheres. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 1, pp.12-23. DOI 10.23671/VNC.2014.1.7418
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