Abstract
In this paper we characterize the circular domains (or the ball) by examining the commutators between a real tangential vector field T (T = Jn(z) for characterizing the ball, where n(z) is the unit outward normal at the boundary point z and J is the complex structure of ) and type-(l,0) vector field L belonging to T1.0(bD). We also give a condition equivalent to dimR Auy(D) ≧1 in terms of a real tangential vector field for any smoothly bounded domain D. with connected boundary and such that condition R holds on D.