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arXiv · 2402.16461

Matrix weighted modulation spaces

Morten Nielsen
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Abstract

Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\mathbb{R}^n)$, $1\leq p<\infty$, we introduce corresponding vector-valued continuous and discrete $\alpha$-modulation spaces $M^{s,\alpha}_{p,q}(W)$ and $m^{s,\alpha}_{p,q}(W)$ and prove their equivalence through the use of adapted tight frames. Compatible notions of molecules and almost diagonal matrices are also introduced, and an application to the study of pseudo-differential operators on vector valued spaces is given.

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Morten Nielsen. 2024-02-26. Matrix weighted modulation spaces. https://arxiv.org/abs/2402.16461

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