A Class of Unbounded Fourier Multipliers on the Unit Complex Ball

Abstract

We introduce a class of Fourier multiplier operators $M_b$ on n-complex unit sphere, where the symbol $b\in H^s(S_{\omega })$. We obtained the Sobolev boundedness of $M_b$. Our result implies that the operators $M_b$ take a role of fractional differential operators on $\partial 𝔹$.