Criteria for R-Boundedness of operator families
The main results state that large classes of
convolution and Fourier multiplier operators
are R-bounded. R-boundedness is of importance
in connection with maximal regularity and
functional calculus. Also shown is that smooth
operator-valued functions have aR-bounded range,
where the degree of smoothness depends on the
geometry of the Banach space.
Primary MSC: 42B15 Multipliers, 44A35 Convolution, 46B09 Probabilistic methods in Banach space theory
Secondary MSC: 47D03 (Semi)groups of linear operators,
Keywords: R-bounded,operator-valued multiplier functions,convolutions on Bochner spaces,UMD
Recent Contributions to Evolution Equations,
Marcel Dekker Lecture Notes in Mathematics.