Embedding with a Lipschitz function

Lipschitz Type Characterizations for Bergman Spaces

We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

POINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS

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...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

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.

Sufficient Conditions for Density in Extended Lipschitz Algebras

1 The Heisenberg group does not admit a bi - Lipschitz embedding into L 1 after

We show that the Heisenberg group, with its Carnot-Caratheodory metric, does not admit a bi-Lipschitz embedding into L1.