Compactness of Hankel operator with symbols of forms

Cheng, Xinbin; Jin, Muzhi; Wang, Q.

doi:10.1007/s10476-020-0029-7

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2020

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“…When the (convex) domain is smooth and satisfies so called maximal estimates 3 , holomorphicity of the symbol along (n − 1)-dimensional analytic (equivalently: affine) polydiscs in the boundary suffices for compactness of the associated Hankel operator. 4 Finally we mention the recent [CJW20], where the authors consider Hankel operators with form symbols (replacing multiplication with the wedge product) and prove many of the results discussed above for this situation.…”

Section: Introduction and Resultsmentioning

confidence: 93%

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: 93%