Sobolev inequalities for (0, q) forms on CR manifolds of finite type

Po Lam Yung

doi:10.4310/MRL.2010.v17.n1.a14

Sobolev inequalities for (0, q) forms on CR manifolds of finite type

Po Lam Yung^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let M²ⁿ⁺¹ (n ≥ 2) be a compact pseudoconvex CR manifold of finite commutator type whose ∂̄_b has closed range in L ² and whose Levi form has comparable eigenvalues. We prove a Gagliardo-Nirenberg inequality for the ∂̄_b complex for (0, q) forms when q ≠ 1 nor n - 1. We also prove an analogous inequality when M satisfies condition Y (q). The main technical ingredient is a new kind of L ¹ duality inequality for vector fields that satisfy Hormander's condition.

Original language	English
Pages (from-to)	177-196
Number of pages	20
Journal	Mathematical Research Letters
Volume	17
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2010.v17.n1.a14
Publication status	Published - Jan 2010
Externally published	Yes

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abstract = "Let M2n+1 (n ≥ 2) be a compact pseudoconvex CR manifold of finite commutator type whose {\=∂}b has closed range in L 2 and whose Levi form has comparable eigenvalues. We prove a Gagliardo-Nirenberg inequality for the {\=∂}b complex for (0, q) forms when q ≠ 1 nor n - 1. We also prove an analogous inequality when M satisfies condition Y (q). The main technical ingredient is a new kind of L 1 duality inequality for vector fields that satisfy Hormander's condition.",

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AB - Let M2n+1 (n ≥ 2) be a compact pseudoconvex CR manifold of finite commutator type whose ∂̄b has closed range in L 2 and whose Levi form has comparable eigenvalues. We prove a Gagliardo-Nirenberg inequality for the ∂̄b complex for (0, q) forms when q ≠ 1 nor n - 1. We also prove an analogous inequality when M satisfies condition Y (q). The main technical ingredient is a new kind of L 1 duality inequality for vector fields that satisfy Hormander's condition.

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Sobolev inequalities for (0, q) forms on CR manifolds of finite type

Abstract

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