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In this paper we study relations between the weighted energy class E χ introduced by S. Benelkourchi, V. Guedj and A. Zeriahi recently with Cegrell's classes E and N . Next we establish a generalized comparison principle for the operator M χ . As an application, we prove a version of existence of solutions of Monge-Ampère type equations in the class E χ (H, ).

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ABSTRACT. In this paper we study q-subharmonic and q-plurisubharmonic functions in C n . Next as an application, we give the notion of q-convex domains in C n which is an extension of weakly q-convex domains introduced and investigated in [10]. In the end of the paper we show that the q-convexity is the local property and give some examples about q-convex domains.

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