New thoughts on old results of R. T. Seeley (Q1434162)

The authors prove the existence of a bounded \(H^\infty\)-calculus in \(L^p\) for a vector-valued elliptic boundary value problem \((A,B_j)\), \(1< p<\infty\), provided that the top-order coefficients of \(A\) are Hölder continuous. To this end the authors use an abstract perturbation result for operators admitting bounded \(H^\infty\)-calculus and kernel estimates for the solution of \((A,B_j)\).