Interpolation of bilinear operators between Banach function spaces (Q1566954)

In this paper the authors study the interpolation properties of bilinear operators between couples of Banach function spaces. We mention only the main result: Let \(E\) be a symmetric space on \(\mathbb R_{+}\) such that \(\min\{1,\frac{1}{t}\}\in E\) and let \(X_{j}=X_{j}(\mu_{j}),\) \(j=1,2,3\) be Banach lattices with \(X_{2}\) a symmetric space on a nonatomic measure space such that \(\phi_{X_{2}} (0+)=0.\) If \(T:(X_{1},L_{\infty})\times (X_{2},L_{\infty})\to (X_{3},L_{\infty}),\) then \(T\) is a bounded bilinear operator from \((X_{1},L_{\infty})_{\Phi}\times \Lambda(\psi)_{a}\) into \((X_{3},L_{\infty})_{\Phi},\) where \(\Phi=E(\frac{1}{t}),\) \(\psi(s)=||D_{\phi(s)}||_{E\to E}\) and \(\phi(s)=\phi_{X_{2}}(s)\) for \(s>0.\)