Triebel–Lizorkin space

Summary

A Triebel–Lizorkin space $F^s_{p,q}(\R^n)$ is a space of tempered distributions defined, like a Besov space, by splitting the Fourier transform into dyadic frequency shells. The difference is the order of the norms. One first takes an $\ell^q$ sum over the shells at each point, and then the $L^p$ norm in space. The scale contains the Lp spaces for $1 < p < \infty$, the Sobolev spaces $W^{k,p}$ for $1 < p < \infty$, and the local Hardy spaces. It gives one framework for many function spaces of harmonic analysis and partial differential equations.