کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590908 | 1334994 | 2013 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Compact composition operators on the Dirichlet space and capacity of sets of contact points
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We prove several results about composition operators on the Dirichlet space D⁎. For every compact set K⊆∂D of logarithmic capacity , there exists a Schur function φ both in the disk algebra A(D) and in D⁎ such that the composition operator Cφ is in all Schatten classes Sp(D⁎), p>0, and for which . For every bounded composition operator Cφ on D⁎ and every ξ∈∂D, the logarithmic capacity of is 0. Every compact composition operator Cφ on D⁎ is compact on BΨ2 and on HΨ2; in particular, Cφ is in every Schatten class Sp, p>0, both on H2 and on B2. There exists a Schur function φ such that Cφ is compact on HΨ2, but which is not even bounded on D⁎. There exists a Schur function φ such that Cφ is compact on D⁎, but in no Schatten class Sp(D⁎).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 264, Issue 4, 15 February 2013, Pages 895-919
Journal: Journal of Functional Analysis - Volume 264, Issue 4, 15 February 2013, Pages 895-919