Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899816 | Journal of Mathematical Analysis and Applications | 2018 | 33 Pages |
Abstract
Let H={zâC:Imz>0} be the upper half plane, and denote by Lp(R), 1â¤p<â, the usual Lebesgue space of functions on the real line R. We define two “composition operators” acting on Lp(R) induced by a Borel function Ï:RâHâ¾, by first taking either the Poisson or Borel extension of fâLp(R) to a function on Hâ¾, then composing with Ï and taking vertical limits. Classical composition operators, induced by holomorphic functions and acting on the Hardy spaces Hp(H) of holomorphic functions, correspond to a special case. Our main results provide characterizations of when the operators we introduce are bounded or compact on Lp(R), 1â¤p<â. The characterization for the case 1
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Boo Rim Choe, Hyungwoon Koo, Wayne Smith,