H 1 -calculus for Generators of Bounded C 0 -groups and Positive Contraction Semigroups on L P -spaces
نویسنده
چکیده
Let A be a generator of a bounded C 0-group, resp. of a positive contraction semi-group, on L p ((), 1 < p < 1. By means of the transference principle of Coifman and Weiss it is shown that A admits an H 1-calculus on each cone C = f 2 C : j arg =2j < g, > 0 resp. on each sector = f 2 C : j arg j < g with > =2. Several applications of these results are included.
منابع مشابه
Differentiability of convolutions, integrated semigroups of bounded semi-variation, and the inhomogeneous Cauchy problem
If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L1(0, b, X), the convolution of T with f is defined by (T ∗f)(t) = ∫ t 0 T (s)f(t− s)ds. It is shown that T ∗ f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T ∗ f is continuously differentiable for a...
متن کاملFixed-point solutions of variational inequalities for nonexpansive semigroups in Hilbert spaces
Let H be a real Hilbert space and S = {T (s) : 0 ≤ s < ∞} be a nonexpansive semigroup on H such that F (S) 6= ∅. For a contraction f with coefficient 0 < α < 1, a strongly positive bounded linear operator A with coefficient γ̄ > 0. Let 0 < γ < γ̄ α . It is proved that the sequences {xt} and {xn} generated by the iterative method xt = tγf(xt) + (I − tA) 1 λt ∫ λt
متن کاملOn the Weiss Conjecture for Analytic Semigroups
Let T(t) be an analytic semigroup with generator A on some Banach space. Le Merdy in [12] showed the validity of the so-called Weiss conjecture : C ∈ L(D(A), Y ) is an admissible observation operator if and only if {‖C(λI − A)−1‖ Reλ ≥ α for some α > 0} is a bounded set, is equivalent to the finite-time admissibility of the fractional power (−A)1/2 for A. The proof was essentially based on the ...
متن کاملUnbounded functional calculus for bounded groups with applications
In this paper, we develop the unbounded extension of the Hille–Phillips functional calculus for generators of bounded groups. Mathematical applications include the generalised Lévy–Khintchine formula for subordinate semigroups, the analyticity of semigroups generated by fractional powers of group generators, where the power is not an odd integer, and a shifted abstract Grünwald formula. We also...
متن کاملDecomposition of H*-Algebra Valued Negative Definite Functions on Topological *-Semigroups
In the present paper, among other results, a decomposition formula is given for the w-bounded continuous negative definite functions of a topological *-semigroup S with a weight function w into a proper H*-algebra A in terms of w-bounded continuous positive definite A-valued functions on S. A generalization of a well-known result of K. Harzallah is obtained. An earlier conjecture of the author ...
متن کامل