# SUBNORMALITY OF S2(a, b, c, d) AND ITS BERGER MEASURE

Duan, Yongjiang;Ni, Jiaqi

• Received : 2015.06.21
• Published : 2016.05.31
• 16 2

#### 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

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#### Acknowledgement

Supported by : NSFC