Norm-generating pseudodifferential operators in the spaces \(W_p^s (\mathbb{R}^n)\) (Q2783067)

Let \(s\geq 0\), \(1<p< \infty\), \(\frac{1}{p} + \frac{1}{p'} =1\). Let \(W^s_p ({\mathbb R}^n)\) be the well-known Sobolev-Slobodeckij spaces. A mapping \(A\) from \(W^s_p ({\mathbb R}^n)\) into its dual \(W^{-s}_{p'} ({\mathbb R}^n)\) is called norm-generating if NEWLINE\[NEWLINE (Au,u) = \|Au |W^{-s}_{p'} ({\mathbb R}^n) \|\cdot \|u |W^s_p ({\mathbb R}^n) \|, \quad u \in W^s_p ({\mathbb R}^n). NEWLINE\]NEWLINE It is the aim of this paper to study the structure of these operators \(A\).NEWLINENEWLINEFor the entire collection see [Zbl 0981.00017].