×

Some remarks on complex powers of (-\(\Delta\) ) and UMD spaces. (English) Zbl 0703.47024

If \(\Delta\) denotes the Laplacian operator and X a Banach space, we prove that if \((-\Delta)^{is}\otimes Id_ x\) is a bounded operator on \(L^ 2({\mathbb{R}};x)\) for all \(s\in {\mathbb{R}}\), then X is a UMD space.

MSC:

47B38 Linear operators on function spaces (general)
60G46 Martingales and classical analysis
46E40 Spaces of vector- and operator-valued functions
47A50 Equations and inequalities involving linear operators, with vector unknowns
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47F05 General theory of partial differential operators
PDFBibTeX XMLCite