We consider the Riesz transforms ∇L−1/2, where L ≡ −divA(x)∇, and A is an accretive, n× n matrix with bounded measurable complex entries, defined on Rn. We establish boundedness of these operators on Lp(Rn), for the range pn < p ≤ 2, where pn = 2n/(n + 2), n ≥ 2, and we obtain a weak-type estimate at the endpoint pn. The case p = 2 was already known: it is equivalent to the solution of the squa...

Suppose X is a real Banach space and F,K : X → X are accretive maps. Under different continuity assumptions on F and K such that the inclusion 0 = u+KFu has a solution, iterative methods are constructed which converge strongly to such a solution. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X . Our method of proof is of independ...

This article is concerned with maximal accretive realization of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible bou...

We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if A is the accretive operator associated with an accretive sesquilinear form A(·, ·) defined on a Hilbert space V contained in L(Ω), we approximate A for β ∈ (0, 1). The fractional powers are defined in terms of the so-called Balakrishnan integral formula. Given a finite element approximatio...