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Journal of Operator Theory

Volume 73, Issue 1, Winter 2015  pp. 159-185.

On Hoermander-Kato spaces

Authors:  Gruia Arsu
Author institution:Institute of Mathematics of The Romanian Academy, P.O. Box 1-174, RO-014700, Bucharest, Romania

Summary: We study an increasing family of spaces $ \{ \mathcal{B}_{k}^{p} \} _{1\leqslant p\leqslant \infty }$ by adapting the techniques used in the study of Beurling algebras by Coifman and Meyer (Au del\`{a} des op\'{e}rateurs pseudo-diff\'{e}rentiels, \textit{Asterisque} \textbf{57}(1978)). Also we study the Schatten-von Neumann properties of pseudo-differential operators with symbols in the spaces $\mathcal{B}_{k}^{p}$.

Keywords: Sobolev-Kato spaces, pseudo-differential operators, Schatten-von Neumann, Wiener amalgam spaces

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