Real interpolation with weighted rearrangement invariant Banach function spaces

Ralph Chill, Sebastian Krol

Published 2015-03-19Version 1

Extending some work of Bennett and Bastero, Milman \& Ruiz, and motivated by recent applications of weighted norm inequalities to maximal regularity of first order Cauchy problems, we define real interpolation spaces on the basis of weighted rearrangement invariant Banach function spaces. We show equivalence of the trace method and the $K$-method, identify real interpolation spaces between a Banach space and the domain of a sectorial operator, and prove an extension of Dore's theorem on the boundedness of $H^\infty$-functional calculus to the weighted rearrangement invariant setting.