A proof of hypoellipticity for Kohn’s operator via FBI

Chinni, Gregorio

doi:10.4171/rmi/647

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High Regularity Upper Bounds1

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2018

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“…For n > 1, b is analytic hypoelliptic on (0, 1) forms, for any C ω , strictly pseudoconvex CR structure. Proofs of this and/or closely related results can be found in [7], [12], [18], [19], [22]. Identifying B ⊂ C n with a ball in R 2n , we regard B × R as a subset of R 2n+1 , hence as a totally real submanifold of C 2n+1 .…”

Section: High Regularity Upper Boundsmentioning

confidence: 99%

Upper Bounds for Bergman Kernels Associated to Positive Line Bundles with Smooth Hermitian Metrics

Christ

2018

Algebraic and Analytic Microlocal Analysis

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Off-diagonal upper bounds are established away from the diagonal for the Bergman kernels associated to high powers L λ of holomorphic line bundles L over compact complex manifolds, asymptotically as the power λ tends to infinity. The line bundle is assumed to be equipped with a Hermitian metric with positive curvature form, which is C ∞ but not necessarily real analytic. The bounds are of the form exp (−h(λ) √ λ log λ) where h → ∞ at a non-universal rate. This form is best possible.

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Section: High Regularity Upper Boundsmentioning

confidence: 99%