Approximation property and nuclearity on mixed-norm L-p, modulation and Wiener amalgam spaces

作者：Delgado, J.^*; Ruzhansky, M.; Wang, B.

来源：Journal of the London Mathematical Society-Second Series, 2016, 94(2): 391-408.

DOI：10.1112/jlms/jdw040

• VON-NEUMANN PROPERTIES
• PSEUDODIFFERENTIAL-OPERATORS
• CONTINUITY PROPERTIES
• BANACH-SPACES
• CALCULUS
• DETERMINANTS

In this paper, we first prove the metric approximation property for weighted mixed-norm L-p spaces. Using Gabor frame representation, this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck's theory becomes applicable, and we give criteria for nuclearity and -nuclearity for operators acting on these spaces as well as derive the corresponding trace formulae. Finally, we apply the notion of nuclearity to functions of the harmonic oscillator on modulation spaces.

• 出版日期2016-10
• 单位北京大学