Bi-parameter pseudo-differential operators in bi-parameter Triebel-Lizorkin and Besov Spaces

In this paper, we mainly establish the $F^{(s_1,s_2)}_{p,q}(\mathbb{R}^{n_1}\times\mathbb{R}^{n_2})$ and $B^{(s_1,s_2)}_{p,q}(\mathbb{R}^{n_1}\times\mathbb{R}^{n_2})$ boundedness of the bi-parameter pseudo-differential operator, where the symbol involved is given by the standard symbols of the H\"{o}rmander class $BS^{(m_1,m_2)}_{(1,1),(\delta_1,\delta_2)}(\mathbb{R}^{2n_1}\times\mathbb{R}^{2n_2})$ for $-\infty Mathematics Subject Classification 42B15, 42B25.