W*-algebras and invariant functionals
Weak Kato-Inequalities and Positive Semigroups.
Weak type (1,1) estimates of the maximal function for the Laguerre semigroup in finite dimensions.
We prove that, in arbitrary finite dimensions, the maximal operator for the Laguerre semigroup is of weak type (1,1). This extends Muckenhoupt's one-dimensional result.
Weighted convolution algebras and their homomorphisms
Weighted norm estimates and -spectral independence of linear operators
We investigate the -spectrum of linear operators defined consistently on for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the -spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω,μ); the balls with respect to this semi-metric are required to satisfy a subexponential volume growth condition. We show how previous results on -spectral independence can be treated...
Well-posedness of abstract Cauchy problems.