@article{Huang2023, 
author = {Long Huang and Xiaofeng Wang},
title = {Schur's test, Bergman-type operators and Gleason's problem on radial-angular mixed spaces},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {10},
pages = {6027-6044},
keywords = {Schur's test, Bergman-type operator, Gleason's problem},
url = {https://www.sciopen.com/article/10.3934/era.2023307},
doi = {10.3934/era.2023307},
abstract = {Let    0  <  p  ,  q  <  ∞,    Φ be a generalized normal function and        L          p      ,      q        (  Φ  ) the radial-angular mixed space. In this paper, we first generalize the classical Schur's test to radial-angular mixed spaces setting and then find the sufficient and necessary condition for the boundedness of integral operators from        L                  p        1            ,              p        2              (  Φ  ) to        L                  q        1            ,              q        2              (  Φ  ) for    1  ≤      p    i    ,      q    i    ≤  ∞ with    i  ∈  {  1  ,  2  }. Moreover, we also establish the boundedness of Bergman-type operators        P          s      ,      t      , where    s  ∈            R       and    t  >  0, on holomorphic radial-angular mixed space        H          p      ,      q        (  Φ  ) for all possible    0  <  p  ,  q  <  ∞. As an application, we finally solve Gleason's problem on        H          p      ,      q        (  Φ  ) for all possible    0  <  p  ,  q  <  ∞.}
}