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Linear Combinations of Composition Operators on the Fock-Sobolev Spaces

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Abstract

We study linear combinations of composition operators acting on the Fock-Sobolev spaces of several variables. We show that such an operator is bounded only when all the composition operators in the combination are bounded individually. In other words, composition operators on the Fock-Sobolev spaces do not possess the same cancelation properties as composition operators on other well-known function spaces over the unit disk. We also show the analogues for compactness and the membership in the Schatten classes. In particular, compactness and the membership in some/all of the Schatten classes turn out to be the same.

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Authors and Affiliations

  1. Department of Mathematics, Pusan National University, Pusan, 609-735, Republic of Korea

    Hong Rae Cho

  2. Department of Mathematics, Korea University, Seoul, 136-713, Republic of Korea

    Boo Rim Choe & Hyungwoon Koo

Authors
  1. Hong Rae Cho
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  2. Boo Rim Choe
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  3. Hyungwoon Koo
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Correspondence to Hyungwoon Koo.

Additional information

H. Cho was supported by NRF of Korea (2011-0013740), B. Choe was supported by NRF of Korea (2013R1A1A2004736) and H. Koo was supported by NRF of Korea (2012R1A1A2000705) and NSFC (11271293).

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Cho, H.R., Choe, B.R. & Koo, H. Linear Combinations of Composition Operators on the Fock-Sobolev Spaces. Potential Anal 41, 1223–1246 (2014). https://doi.org/10.1007/s11118-014-9417-6

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  • DOI: https://doi.org/10.1007/s11118-014-9417-6

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