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 Subnormality of $S_{2}(a,b,c,d)$ and its Berger measure Bull. Korean Math. Soc. 2016 Vol. 53, No. 3, 943-957 https://doi.org/10.4134/BKMS.b150486Published online May 31, 2016 Yongjiang Duan and Jiaqi Ni Northeast Normal University, Northeast Normal University Abstract : We introduce a 2-variable weighted shift, denoted by $S_2(a,b$, $c,d)$, which arises naturally from analytic function space theory. We investigate when it is subnormal, and compute the Berger measure of it when it is subnormal. And we apply the results to investigate the relationship among 2-variable subnormal, hyponormal and 2-hyponormal weighted shifts. Keywords : subnormal, $S_{2}(a,b,c,d)$, Berger measure, 2-variable weighted shift, hyponormal, $k$-hyponormal MSC numbers : 47B20, 47B37, 47B38, 47A13 Full-Text :