Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group
نویسندگان
چکیده
منابع مشابه
Maximum and Comparison Principles for Convex Functions on the Heisenberg Group
The purpose in this paper is to establish pointwise estimates for a class of convex functions on the Heisenberg group. An integral estimate for classical convex functions in terms of the Monge–Ampère operator det D2u was proved by Aleksandrov, see [3, Theorem 1.4.2]. Such estimate is of great importance in the theory of weak solutions for the Monge–Ampère equation, and its proof revolves around...
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2015
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2015.08.014