Abstract
Let E be a translation invariant Banach function space over an infinite compact abelian group G and Mφ be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection invariant (which ensures that φ̄ is also a multiplier symbol for E). The following Fuglede type theorem is established. Whenever T is a bounded linear operator on E satisfying MφT=TMφ, then also Mφ̄T=TMφ̄.
Original language | English |
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Pages (from-to) | 259-273 |
Number of pages | 15 |
Journal | Indagationes Mathematicae |
Volume | 34 (2023) |
Issue number | 2 |
DOIs | |
Publication status | Published - 2022 |
Keywords
- Compact abelian group
- Fourier multiplier operator
- Reflection invariance
- Translation invariant Banach function space