An invariant variant of the little Grothendieck theorem for Sobolev spaces

Abstract

We prove that every Hilbert space operator which factorizes invariantly through Sobolev space $W_1^1({\mathbb{T}}^d)$ belongs to some non-trivial Schatten class.

Changes in v2: slightly different title, corrected exponent in the statement of Theorem 2 and Lemma 2