I am trying to understand periodic Lebesgue spaces $L^p(\mathbb{T})$.
In particular, I have trouble understanding how the scaling $[\delta_\lambda f](x) = f(\lambda x)$ and translation $[\tau_h f](x) = f(x+h)$ are defined.
What do I have to keep in mind when studying these two mappings on the torus?
It seems to be natural to me that for example $\| f \|_p = \| \tau_h f \|_p$ for all $h$. Is that true?
If you could share any insight or references with me that would bei highly appreciated.