Bulletin of the
Korean Mathematical Society BKMS

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