A note on the subsolution theorem in weighted energy classes of m-subharmonic functions with given boundary values
Abstract
In this note, we deal with the existence of solutions of the weighted complex m-Hessian equation -χ(u)Hm(u)=μ in the class Em,χ(f,Ω) if there exists a subsolution in this class, where the given boundary value f∈Em(Ω) MSHm(Ω). This is a generalization of the result in the paper PDtaiwan where we proved that the subsolution theorem is true in the class Em,χ(f,Ω) in the case when the given boundary value f∈Nm(Ω) MSHm(Ω).
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