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

Abstract

In the framework of Hardy spaces H p , 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 H p to BMO, and from BMO to BMO.

Keywords

• convolution
• sphere
• oscillating symbol
• bmo
• (hp− hq)-estimates
• multiplier
• distribution