Melin-Hörmander inequality in a Wiener type pseudodifferential algebra
The main result of this paper is the proof of a Melin-Hörmander inequality for the Banach algebra of pseudo-differential operators associated to the class of symbols \(\Sigma ,\) consisting of elements \(a\in S^{\prime }(\mathbb{R}^{2n})\) such that \[ \sup_{Y\in \mathbb{R}^{2n}}\left| \widehat{\varphi _{Y}a}(X)\right| \in L^{1}(dX) , \] where \(\varphi \in S(\mathbb{R}^{2n})\backslash \left\{ 0\right\} ,\varphi _{Y}(\cdot )=\varphi (\cdot -Y)\) for \(Y\in \mathbb{R}^{2n},\) and \(\widehat{a} \) denotes the Fourier transform of \(a.\)
Banach algebra of pseudo-differential operators
scientific article; zbMATH DE number 2062424
scientific article