TY - UNPB
T1 - Matrix weighted modulation spaces
AU - Nielsen, Morten
PY - 2024/2/26
Y1 - 2024/2/26
N2 - Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\bR^n)$, $1\leq p<\infty$, 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.
AB - Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\bR^n)$, $1\leq p<\infty$, 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.
KW - math.FA
KW - Primary 42C40, 42C15, Secondary 42B15
M3 - Preprint
BT - Matrix weighted modulation spaces
ER -