UMD Banach spaces and the maximal regularity for the square root of several operators

Abstract

In this paper we prove that the maximal L p -regularity property on the interval (0, T ), T > 0, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on L 2 (Ω, dµ; X), characterizes the UMD property for the Banach space X. t 0 ∂ t T t−s (f (s))ds, t > 0. Since ∂ t T t L(B) ≤ C/t, t > 0, where L(B) denotes the space of bounded operators from B into itself, the convergence of the integral in (2) depends on the properties of f . Suppose that Date: Saturday 10 th November, 2018. 2010 Mathematics Subject Classification. 47D06, 35B65, 42B25.