A Note on the Poincaré Inequality for Lipschitz Vector Fields of Step Two
نویسندگان
چکیده
We provide a Poincaré inequality for families of Lipschitz continuous vector fields satisfying a Hörmander-type condition of step two.
منابع مشابه
On the character space of vector-valued Lipschitz algebras
We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...
متن کاملPOINT 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...
متن کاملWeighted Multilinear Poincaré Inequalities for Vector Fields of Hörmander Type
Abstract. As the classical (p, q)-Poincaré inequality is known to fail for 0 < p < 1, we introduce the notion of weighted multilinear Poincaré inequality as a natural alternative when m-fold products and 1/m < p are considered. We prove such weighted multilinear Poincaré inequalities in the subelliptic context associated to vector fields of Hörmader type. We do so by establishing multilinear re...
متن کاملOn the uniform Poincaré inequality
We give a proof of the Poincaré inequality in W (Ω) with a constant that is independent of Ω ∈ U , where U is a set of uniformly bounded and uniformly Lipschitz domains in R. As a byproduct, we obtain the following : The first non vanishing eigenvalues λ2(Ω) of the standard Neumann (variational) boundary value problem on Ω for the Laplace operator are bounded below by a positive constant if the...
متن کاملEmbedding Theorems into Lipschitz and Bmo Spaces and Applications to Quasilinear Subelliptic Differential Equations
This paper proves Harnack’s inequality for solutions to a class of quasilinear subelliptic differential equations. The proof relies on various embedding theorems into nonisotropic Lipschitz and BMO spaces associated with the vector fields X1, . . . , Xm satisfying Hörmander’s condition. The nonlinear subelliptic equations under study include the important p-sub-Laplacian equation, e.g.,
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009