@article{He2023, 
author = {Li He},
title = {Composition operators on Hardy-Sobolev spaces with bounded reproducing kernels},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {2708-2719},
keywords = {reproducing kernel, automorphism, Hardy-Sobolev space, composition operator},
url = {https://www.sciopen.com/article/10.3934/math.2023142},
doi = {10.3934/math.2023142},
abstract = {For any real    β let        H    β    2   be the Hardy-Sobolev space on the unit disc              D      .        H    β    2   is a reproducing kernel Hilbert space and its reproducing kernel is bounded when    β  >  1      /    2. In this paper, we prove that        C          φ       has dense range in        H          β              2       if and only if the polynomials are dense in a certain Dirichlet space of the domain    φ  (            D        ) for    1      /    2  <  β  <  1. It follows that if the range of        C          φ       is dense in        H          β              2      , then    φ is a weak-star generator of        H          ∞      , although the conclusion is false for the classical Dirichlet space        D  . Moreover, we study the relation between the density of the range of        C          φ       and the cyclic vector of the multiplier        M          φ              β        .}
}