In this paper, we determine the character space of vector-valued Lipschitz algebra Lipd(X, E), where (X, d) is any metric and E a certain unital semisimple commutative *-Banach algebra.

The derivation of a Hardy field induces on its value group a certain function ψ. If a Hardy field extends the real field and is closed under powers, then its value group is also a vector space over R. Such “ordered vector spaces with ψ-function” are called H-couples. We define closed H-couples and show that every H-couple can be embedded into a closed one. The key fact is that closed H-couples ...

In the framework of Hardy type inequalities and their applications to evolution problems, paper deals with local nonlocal weighted improved related study Kolmogorov operators perturbed by singular potentials. The class weights is wide enough. We focus our attention on potentials obtained inverse square adding a nonnegative correction term. method used get results based introduction suitable vec...

Let ( X , ρ μ ) $({\mathcal {X}},\rho ,\mu )$ be a space of homogeneous type in the sense Coifman and Weiss, let Y $Y({\mathcal {X}})$ ball quasi-Banach function on ${\mathcal {X}}$ which supports both Fefferman–Stein vector-valued maximal inequality boundedness powered Hardy–Littlewood operator its associate space. The authors first introduce Hardy H ∗ $H_{Y}^*({\mathcal associated with via gr...

Modeled on the Gauss measure, the authors introduce the locally doubling measure metric space X, d, μ ρ, which means that the set X is endowed with a metric d and a locally doubling regular Borel measure μ satisfying doubling and reverse doubling conditions on admissible balls defined via the metric d and certain admissible function ρ. The authors then construct an approximation of the identity...

The statement of the problem. In this paper we study weighted norm inequalities with matrix valued weights. Namely, let W be a d × d matrix weight, i.e. a L-function whose values are selfadjoint nonnegative d × d matrices. We suppose that the weight W is defined on the unit circle T = {z ∈ C : |z| = 1} or the real line R. Let L = L(C) be the space of all measurable vector functions on T whose C...

Recent work has demonstrated that Clark’s theory of unitary perturbations of the backward shift restricted to a deBranges-Rovnyak subspace of Hardy space on the disk has a natural extension to the several variable setting. In the several variable case, the appropriate generalization of the Schur class of contractive analytic functions is the closed unit ball of the Drury-Arveson multiplier alge...