The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let  be a non-emp...

our aim in this paper is to prove an analog of younis's theorem on the image under the jacobi transform of a class functions satisfying a generalized dini-lipschitz condition in the space $mathrm{l}_{(alpha,beta)}^{p}(mathbb{r}^{+})$, $(1< pleq 2)$. it is a version of titchmarsh's theorem on the description of the image under the fourier transform of a class of functions satisfying the dini-lip...

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.

A charge in a compact metric space is a continuous linear functional on the space of normal chains with real coefficients equipped with a modified flat norm topology. Charges form a cochain complex whose cohomology reflects metric, rather than topological, properties of metric spaces. Elaborating on an idea of De Giorgi, we construct a normed graded differential algebra of Lipschitz forms in a ...

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C Finsler manifold M is determined by the normed algebra C b (M) of all real-valued, bounded and C k smooth functions with bounded derivative defined on M . As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C Finsler manifold M is determined by the algebra...

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

We use the canonical Lipschitz geometry available on the boundary of a hyperbolic group to construct finitely summable Fredholm modules over the crossed product of the boundary action. The procedure yields a full set of representatives of the K-homology of the crossed product, and all of them are p-summable for p in an appropriate range related to the geometry of the boundary. By restricting th...

The well-known Lawvere category [0,∞] of extended real positive numbers comes with a monoidal closed structure where the tensor product is the sum. But [0,∞] has another such structure, given by multiplication, which is *-autonomous and a CL-algebra (linked with classical linear logic). Normed sets, with a norm in [0,∞], inherit thus two symmetric monoidal closed structures, and categories enri...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

The purpose of this article is to establish Jackson-type inequality in the polydiscs UN of C for holomorphic spaces X, such as Bergman-type spaces, Hardy spaces, polydisc algebra and Lipschitz spaces. Namely, E k(f,X) (−→ 1/k, f,X ) , where E k(f,X) is the deviation of the best approximation of f ∈ X by polynomials of degree at most kj about the jth variable zj with respect to the X-metric and ...