It is shown that a Banach space E has type p if and only for some (all)
dβ₯1 the Besov space Bp,p(p1ββ21β)dβ(Rd;E) embeds into the
space \g(L^2(\R^d),E) of \g-radonifying operators L2(Rd)βE. A
similar result characterizing cotype q is obtained. These results may be
viewed as E-valued extensions of the classical Sobolev embedding theorems.Comment: To appear in Mathematische Nachrichte