# reference request – Multivarate “RKHS” Examples

I’ve been reading about RKHSs and Hilbert spaces of functions these days a bit these days and I haven’t yet come across an example of a hilbert space $$H$$ whose elements are all functions $$f:mathbb{R}^nrightarrow mathbb{R}^m$$ for $$n,m>1$$ and for which the evaluation functions $$E_x:fmapsto f(x)$$ are bounded.

Do such objects exist and if so what are some well-known examples?

The only thing I have at the moment is the space of $$ntimes m$$ matrices with Frobenius norm…which is a bit underwhelming…