@article{Jiang2025, 
author = {Zhi-jie Jiang},
title = {Weighted composition operators between vector-valued Bloch-type spaces on the polydisk},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18957-18982},
keywords = {unit polydisk, vector-valued Bloch-type space, weighted composition operator, boundedness, compactness},
url = {https://www.sciopen.com/article/10.3934/math.2025847},
doi = {10.3934/math.2025847},
abstract = {Let    X and    Y be two complex Banach spaces,                      C              N   the    N-dimensional complex Euclidean space with the inner product    ⟨  z  ,  w  ⟩  =      ∑          l      =      1        N        z    l              w      l        ¯   and                      D              N   the unit polydisk in                      C              N  . Let        φ   be a holomorphic self-map of                      D              N   and    u  ∈  H  (                    D              N    ,      L    (  X  ,  Y  )  ), where    H  (                    D              N    ,  X  ) denotes the space of all vector-valued holomorphic functions on                      D              N   and        L    (  X  ,  Y  ) denotes the space of all bounded linear operators from    X to    Y. The weighted composition operator        W          u      ,              φ              :  H  (                    D              N    ,  X  )  →  H  (                    D              N    ,  Y  ) is defined by                                 W                      u            ,                          φ                                      f        (        z        )        =        u        (        z        )        (        f        (                  φ                (        z        )        )        )        .            The bounded and compact weighted composition operators between vector-valued Bloch-type spaces on the unit polydisk are completely characterized in the paper.}
}