A Remark Related Pseudo-Differential Operators on Multi-Parameter Besov-Lipschitz and Triebel-Lizorkin Spaces

Abstract

Let a symbol $\sigma \left(x,\xi \right)$ belongs to the class ${\mathcal{S}}_{\left(1,1\right),\left({\delta }_1,{\delta }_2\right)}^{\left(0,0\right)}$ with $x,\xi \in {ℝ}^{n_1}\times {ℝ}^{n_2}$ and $0\le {\delta }_1,{\delta }_2<1$ . This paper mainly establish the boundedness of the class of all bi-parameter pseudo-differential operators associated with the symbol $\sigma \left(x,\xi \right)$ on the multi-parameter non-homogeneous Besov-Lipschitz and Triebel-Lizorkin spaces.