@article{Xu2023, 
author = {Yun Xu and Shanli Ye},
title = {A Derivative Hilbert operator acting from Bergman spaces to Hardy spaces},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {9290-9302},
keywords = {Derivative-Hilbert operator, Bergman space, Hardy space, Carleson measure},
url = {https://www.sciopen.com/article/10.3934/math.2023466},
doi = {10.3934/math.2023466},
abstract = {Let    μ be a positive Borel measure on the interval    [  0  ,  1  ). The Hankel matrix              H              μ        =  (      μ          n      ,      k            )          n      ,      k      ≥      0       with entries        μ          n      ,      k        =      μ          n      +      k      , where        μ          n        =      ∫          [      0      ,      1      )            t    n    d  μ  (  t  ), formally induces the operator as follows:               D      H        μ    (  f  )  (  z  )  =      ∑          n      =      0        ∞        (                  ∑                  k          =          0                ∞                    μ                  n          ,          k                            a        k              )    (  n  +  1  )      z    n    ,    z  ∈      D    ,where    f  (  z  )  =      ∑          n      =      0        ∞        a    n        z    n   is an analytic function in        D  . In this article, we characterize those positive Borel measures on    [  0  ,  1  ) such that              D      H        μ   is bounded (resp., compact) from Bergman spaces              A        p   into Hardy spaces        H    q  , where    0  <  p  ,  q  <  ∞.}
}