广义Bergman空间上的紧复合算子
Compact Composition Operators on Generalized Bergman Spaces
首先证明广义Bergman空间AN,αp,(α>-n-1,p>0)上的复合算子Cφ的有界性和紧性是不依赖于p的,进而证明了若对某个 q> 0=和-n-1 < β < α,Cφ在AN,βp上有界,则Cφ在AN,αp,(α>-n-1,p>0)上是紧的当且仅当lim|z|→1-((1-|z|2)/(1-|φ(z)|2))=0.
We prove that the boundedness and compactness of the composition operators Cφ on generalized Bergman spaces AN,αp,(α>-n-1,p>0) are independent of p. On this foundation, we prove that if Cφ is bounded on AN,βp for some q> 0 and -n-1 < β < α, then Cφ is compact on AN,αp,(α>-n-1,p>0) if and only if lim|z|→1-((1-|z|2)/(1-|φ(z)|2))=0.
复合算子 / 广义Bergman空间 / 有界性 / 紧性 {{custom_keyword}} /
composition operator / generalized Bergman space / boundedness / compactness {{custom_keyword}} /
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国家自然科学基金资助项目(11501136);广东第二师范学院博士基金资助项目(2014ARF04)
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