On singular values of Hankel operators on Bergman spaces
نویسندگان
چکیده
In this paper, we study the behavior of singular values Hankel operators on weighted Bergman spaces Aωφ2, where ωφ=e−φ and φ is a subharmonic function. We consider compact Hϕ‾, with anti-analytic symbols ϕ‾, give estimates trace h(|Hϕ‾|) for any convex function h. This allows us to asymptotic (sn(Hϕ‾))n in terms nonincreasing rearrangement |ϕ′|/Δφ respect an adequate measure. For radial weights, first prove that critical decay achieved by (sn(Hz‾))n. Namely, establish if sn(Hϕ‾)=o(sn(Hz‾)), then Hϕ‾=0. Then, show Δφ(z)≍1(1−|z|2)2+β β≥0, sn(Hϕ‾)=O(sn(Hz‾)) only ϕ′ belongs Hardy space Hp, p=2(1+β)2+β. Finally, compute asymptotics sn(Hϕ‾) whenever ϕ′∈Hp.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2022
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2022.109521