Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki (Jun 2011)

Estimates for some convolution operators with singularities of their kernels on spheres

  • V. A. Nogin,
  • A. I. Zadorozhnyi,
  • A. V. Gil

DOI
https://doi.org/10.14498/vsgtu848
Journal volume & issue
Vol. 2(23)
pp. 17 – 23

Abstract

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In the framework of Hardy spaces Hp, we study multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in Rn. Necessary and sufficient conditions are obtained for such operators to be bounded from Hp to Hq, 0<p≤q<∞, from Hp to BMO, and from BMO to BMO.