Hypoelliptic heat kernel inequalities on the Heisenberg group

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Note on the Heat Kernel on the Heisenberg Group

Let ps be the convolution kernel of the operator e −sL (see [5, (1.10), (1.11)]). When s > 0, e−sL is the solution operator for the Heisenberg heat equation ∂su = −Lu and ps is called the heat kernel (see [6, (7.30), p. 71]. The goal of this note is to study the analytic continuation of the heat kernel ps. This is interesting from the point of view of the theory of analytic hypoellipticity (see...

متن کامل

Global Poincaré Inequalities on the Heisenberg Group and Applications

Let f be in the localized nonisotropic Sobolev space W 1,p loc (H ) on the n-dimensional Heisenberg group H = C × R, where 1 ≤ p < Q and Q = 2n + 2 is the homogeneous dimension of H. Suppose that the subelliptic gradient is gloablly L integrable, i.e., Hn |∇Hnf |pdu is finite. We prove a Poincaré inequality for f on the entire space H. Using this inequality we prove that the function f subtract...

متن کامل

Sharp constants in several inequalities on the Heisenberg group

We derive the sharp constants for the inequalities on the Heisenberg group H whose analogues on Euclidean space R are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Laplacian and c...

متن کامل

Vertical versus Horizontal Poincaré Inequalities on the Heisenberg Group

Let H = 〈a, b | a[a, b] = [a, b]a ∧ b[a, b] = [a, b]b〉 be the discrete Heisenberg group, equipped with the left-invariant word metric dW (·, ·) associated to the generating set {a, b, a−1, b−1}. Letting Bn = {x ∈ H : dW (x, eH) 6 n} denote the corresponding closed ball of radius n ∈ N, and writing c = [a, b] = aba−1b−1, we prove that if (X, ‖·‖X) is a Banach space whose modulus of uniform conve...

متن کامل

Inequalities between Dirichlet and Neumann Eigenvalues on the Heisenberg Group

Universal eigenvalue inequalities are a classical topic in the spectral theory of differential operators. Most relevant to our work here are comparison theorems between the Dirichlet and Neumann eigenvalues λj(−∆Ω ) and λj(−∆Ω ), j ∈ N, of the Laplacian in a smooth, bounded domain Ω ⊂ R. Note that λj(−∆Ω ) ≤ λj(−∆Ω ) for all j ∈ N by the variational characterization of eigenvalues. This trivial...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2005

ISSN: 0022-1236

DOI: 10.1016/j.jfa.2004.06.012