Hankel operators on the Bergman spaces of Reinhardt domains and foliations of analytic disks

Clos, Timothy G.

doi:10.1007/s12215-019-00425-0

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2020

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“…2 Moreover, for (smooth) convex domains in C 2 , holomorphy of the symbol along analytic discs in the boundary is also sufficient for compactness of the Hankel operator. Further contributions are in [Le10,ČS ¸17,CS ¸18,Clo19]; we refer the reader to the introduction in [CC ¸S ¸18] for a summary. The latter authors significantly reduce the regularity requirements on both the domain (Lipschitz in C 2 or convex in C n ) and the symbol (in C(Ω)) that is required to infer holomorphicity of the symbol along analytic discs in the boundary from compactness of the Hankel operator.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Compactness of Hankel operators with continuous symbols on convex domains

Celik,

Sahutoglu,

Straube

2020

Preprint

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Let Ω be a bounded convex domain in C n , n ≥ 2, 1 ≤ q ≤ (n − 1), and φ ∈ C(Ω). If the Hankel operator H q−1 φ on (0, q − 1)-forms with symbol φ is compact, then φ is holomorphic along q-dimensional analytic (actually, affine) varieties in the boundary. We also prove a partial converse: if the boundary contains only 'finitely many' varieties, 1 ≤ q ≤ n, and φ ∈ C(Ω) is analytic along the ones of dimension q (or higher), then H

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Section: Introduction and Resultsmentioning

confidence: 99%