Analysis in Banach Spaces

Stability properties of stochastic maximal L-regularity

“…In this subsection we briefly review some basic facts regarding γ-radonifying operators; for further discussions see [20,Chapter 9]. Through this subsection (γ n ) n∈N denotes a Gaussian sequence, i.e.…”

“…where we applied the γ-Fubini's theorem (see [20,Theorem 9.4.8]) in ( * ). By Fubini's theorem and Proposition 3.7 we obtain…”

“…Sectorial Operators and H ∞ -calculus. For details on the H ∞ -calculus we refer the reader to [16,20,29]. For ϕ ∈ (0, π) we denote by Σ ϕ := {z ∈ C : | arg(z)| < ϕ} the open sector of angle ϕ.…”

“…where the orientation of ∂Σ ν is such that σ(A) is on the right. By [20,Section 10.2], f (A) is well-defined in L (X) and it is independent of ν ∈ (ω(A), ϕ). Furthermore, the operator A is said to have a bounded H ∞ (Σ ϕ )-calculus if there exists C > 0 such that for all f ∈…”

“…Nowadays it is known that a large class of elliptic operators have a bounded H ∞ -calculus. For instances see [10], [39,Example 3.2], [44,Subsection 1.3], [20,Section 10.8] and in the reference therein.…”