Hilbert space compression for free products and HNN-extensions

We investigate the behavior of equivariant and non-equivariant Hilbert space compression under group constructions. Given the (equivariant or non-equivariant) Hilbert space compression of two groups, we find bounds on the compression of their free product. We also investigate the case of HNN-extensions of a group relative to a subgroup which is finite or of finite index.