Functional calculi for linear operators in vector-valued \(L^p\)-spaces via the transference principle. (English) Zbl 0956.47008

Hieber, Matthias; Prüss, Jan

Adv. Differ. Equ. 3, No. 6, 847-872 (1998).

Via transference principle due to Coifman and Weiss the authors investigate the \(H^\infty\)-calculi for linear operators in vector-valued spaces \(X=L^p(\Omega,\mu,Y)\), \(1<p<\infty\), where \((\Omega,\mu)\) is a measure space and \(Y\) is a Banach space of class \({\mathcal HT}\).

Reviewer: N.Bozhinov (Sofia)

MSC:

47A60	Functional calculus for linear operators
35J25	Boundary value problems for second-order elliptic equations
35J40	Boundary value problems for higher-order elliptic equations
42B15	Multipliers for harmonic analysis in several variables

Keywords:

functional calculus; transference principle