Boundedness of Iterated Spherical Average on α-Modulation Spaces

Abstract

For the iteration of spherical average (A ₁) ^N and the Laplace operator Δ, we consider the boundedness of the operator Δ(A ₁) ^N on the α-modulation spaces $M_{p,q}^{s,\alpha }$. The authors obtain some sufficient and necessary conditions to ensure the boundedness on the α-modulation spaces. The main theorems significantly improve some known results.

Keywords

Spherical average / α-Modulation spaces / Bessel functions