Convolutions of Orlicz spaces and Orlicz Schatten classes, with applications to Toeplitz operators

2025/05/03 by Wolfram Bauer, Bauer, Wolfram, Robert Fulsche +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2505.01707

openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Φ be a Young function. We study convolution properties for symbol classes s_A,Φ, which consist of all a such that the pseudo-differential operator Op _A(a) is in the Orlicz Schatten class \mathscr I _Φ(L²(\mathbf R^d)). Especially we prove Young type results for such classes. We apply the results on Toeplitz operators and prove Orlicz Schatten properties of such operators.

Citations

• Non-isometric translation and modulation invariant Hilbert spaces
• Continuity and Bargmann mapping properties of quasi-Banach Orlicz modulation spaces
• Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey\n type pseudo-differential operators
• Matrix parameterized pseudo-differential calculi on modulation spaces
• Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipović kernels

Related

• Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents
• Convolution structures for an Orlicz space with respect to vector\n measures on a compact group
• Products on Schatten-von Neumann classes and modulation spaces
• On Orlicz Theory
• Localization operators on discrete Orlicz modulation spaces