Calderón-Zygmund theory for operator-valued kernels (Q1092353)

The authors present a new angle of the classical paper of Benedek- Calderón-Panzone on convolution operators on Banach space valued functions; with BMO, UMD, atoms, weights, Littlewood-Paley operators, operators with variable kernels, in the vector-valued setting. From the new results: For every \(\epsilon >0\), there exists \(C_{\epsilon}>0:\) \((T^*f)^{\#}\leq C_{\epsilon}M_{1+\epsilon}f\), \(f\in L_ c^{\infty}\); then \(T^*\) is bounded from \(L_ c^{\infty}\) to BMO. And \[ \int_{R^ n}T^*f(x)^ pw(x)dx\leq C_{p,w}\int_{R^ n}| f(x)|^ pw(x)dx, \] for all \(1<p<\infty\), \(w\in A_ p\).