ON SMOOTHING OF PLURISUBHARMONIC FUNCTIONS ON UNBOUNDED DOMAINS

We prove that for every n >= 2, there exists a pseudoconvex domain S2 subset of Cn such that c0(S2) C c1(S2), where ck(S2) denotes the core of S2 with respect to Ck-smooth plurisubharmonic functions on S2. Moreover, we show that there exists a bounded continuous plurisubharmonic function on S2 that is not the pointwise limit of a sequence of C1-smooth bounded plurisubharmonic functions on S2.