Tensor products of multilinear operators (Q1079787)

The Calderón commutator C(a,f) is a bounded bilinear operator from \(L^{\infty}(R^ 1)\times L^ 2(R^ 1)\) into \(L^ 2(R^ 1)\). Its tensor product with itself is a bounded operator from \(L^{\infty}(R^ 2)\times L^ 2(R^ 2)\) into \(L^ 2(R^ 2)\). The author gives the direct proof of this result due to J. Aguirre and a counterexample showing that tensor products of bounded bilinear operators are not always bounded..