TY - JOUR
T1 - Composition operators on holomorphic Sobolev spaces in Bn
AU - Koo, Hyungwoon
AU - Park, Inyoung
N1 - Funding Information:
✩ This work is partially supported by Korea Research Foundation Grant (KRF-2008-314-C00012).
PY - 2010/9
Y1 - 2010/9
N2 - We study the composition operator CΦ on holomorphic Sobolev spaces induced by an analytic self-map Φ of Bn in Cn that extends to be smooth on Bn. We characterize the boundedness and the compactness of CΦ on Aα,sp, and prove the jump phenomenon of CΦ on Aα,sp. Moreover, we show an interesting result that the boundedness of CΦ on Aα,sp is equivalent to the compactness of CΦ:Aα,sp→Aβ,tq for appropriate Aβ,tq, for example Aβ,tq=Aα+1/4,sp. We provide examples to show that our results are sharp.
AB - We study the composition operator CΦ on holomorphic Sobolev spaces induced by an analytic self-map Φ of Bn in Cn that extends to be smooth on Bn. We characterize the boundedness and the compactness of CΦ on Aα,sp, and prove the jump phenomenon of CΦ on Aα,sp. Moreover, we show an interesting result that the boundedness of CΦ on Aα,sp is equivalent to the compactness of CΦ:Aα,sp→Aβ,tq for appropriate Aβ,tq, for example Aβ,tq=Aα+1/4,sp. We provide examples to show that our results are sharp.
KW - Boundedness
KW - Compactness
KW - Composition operator
KW - Holomorphic Sobolev space
KW - Unit ball
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U2 - 10.1016/j.jmaa.2010.02.056
DO - 10.1016/j.jmaa.2010.02.056
M3 - Article
AN - SCOPUS:77952557230
VL - 369
SP - 232
EP - 244
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -