Continuity of pseudo-differential operators on Bessel and Besov spaces (Q2761696)

The author studies the continuity of pseudo-differential operators on Bessel potential spaces \(H^s_p({\mathbb R}^n)\), and on the Besov spaces \(B^{s,q}_p({\mathbb R}^n)\). The pseudo-differential operators are taken from the Hörmander class \(S^m_{\rho,\delta}\) with an additional condition involving a modulus of continuity \(\omega\), satisfying \(\sum_{j\geq 0} [\omega(2^{-j}\Omega(2^j)]^2< \infty\), where \(\Omega\) is a suitable positive function.