Geodesic
Essential norms of the extended Cesàro operators on Bergman spaces with exponential weight in the unit ball
Filomat, Tome 36 (2022) no. 9, p. 2903

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Let B n = {z ∈ C n : |z| 1} be the unit ball of the complex n-plane C n , a holomorphic function in B n and A 2 α,β (B n) the space of holomorphic functions that are L 2 with respect to a rapidly decreasing weight of form ω α,β (z) = (1 − |z|) α e − β 1−|z| on B n , where α ∈ R and β > 0. In this paper, we compute the essential norm of the extended Cesàro operator T on A 2 α,β (B n). As a direct application, we obtain the essential norm for the one-variable case.
DOI : 10.2298/FIL2209903J
Classification : 47B38, 47B33, 47B37
Keywords: Extended Cesàro operator, Bergman space with exponential weight, Essential norm, Unit ball 
Zhi-Jie Jiang; Zuo-An Li; Xiao-Feng Wang. Essential norms of the extended Cesàro operators on Bergman spaces with exponential weight in the unit ball. Filomat, Tome 36 (2022) no. 9, p. 2903 . doi: 10.2298/FIL2209903J
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     author = {Zhi-Jie Jiang and Zuo-An Li and Xiao-Feng Wang},
     title = {Essential norms of the extended {Ces\`aro} operators on {Bergman} spaces with exponential weight in the unit ball},
     journal = {Filomat},
     pages = {2903 },
     year = {2022},
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     number = {9},
     doi = {10.2298/FIL2209903J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2209903J/}
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