@article{Huang2022, 
author = {Cheng-shi Huang and Zhi-jie Jiang and Yan-fu Xue},
title = {Sum of some product-type operators from mixed-norm spaces to weighted-type spaces on the unit ball},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {18194-18217},
keywords = {product-type operator, boundedness, compactness, mixed-norm space, weighted-type space, essential norm, Hilbert-Schmidt norm},
url = {https://www.sciopen.com/article/10.3934/math.20221001},
doi = {10.3934/math.20221001},
abstract = {Let        u          j       be the holomorphic functions on the open unit ball        B   in              C              n      ,    j  =            0      ,      m        ¯  ,    φ a holomorphic self-map of        B  , and        ℜ          j       the    jth iterated radial derivative operator. In this paper, the boundedness and compactness of the sum operator              S                                u          →                    ,      φ        m    =      ∑          j      =      0        m        M                  u        j                  C    φ        ℜ    j   from the mixed-norm space    H  (  p  ,  q  ,  ϕ  ), where    0  <  p  ,  q  <  +  ∞, and    ϕ is normal, to the weighted-type space        H    μ    ∞   are characterized. For the mixed-norm space    H  (  p  ,  q  ,  ϕ  ),    1  ≤  p  <  +  ∞,    1  <  q  <  +  ∞, the essential norm estimate of the operator is given, and the Hilbert-Schmidt norm of the operator on the weighted Bergman space        A    α    2   is also calculated.}
}