On the weighted m−energy classes

Maximal subextension and approximation of m- subharmonic function

“…Next by Theorem 3.3 in [DT23] we have ũ ∈ E m ( Ω). So H m (ũ j ) converges weakly to H m (ũ) as j → ∞.…”

“…Moreover, by Theorem 3.6 in [DT23] we have if u ∈ E m,χ (Ω) then the m− weighted energy of u is finite i.e., Ω (−χ • u)H m (u) < +∞.…”

“…According to Theorem 3.3 in [DT23], if χ ̸ ≡ 0 then E m,χ (Ω) ⊂ E m (Ω) which means that the complex m− Hessian operator is well -defined on class E m,χ (Ω) and if χ(−t) < 0 for all t > 0 then we have E m,χ (Ω) ⊂ N m (Ω).…”

“…In Section 2 we recall the definitions and results concerning the m-subharmonic functions which were introduced and investigated intensively in the recent years by many authors (see [B l05], [SA12]). We also recall the Cegrell classes of m-subharmonic functions F m (Ω), N m (Ω), E m (Ω) and E m,χ (Ω) which were introduced and studied in [Ch12], [T18], [DBH14] and [DT23]. In Section 3, we present subextension in the class E 0 m (Ω), F m (Ω) and E m,χ (Ω).…”

“…2.7. We recall some results on weighted m− energy classes in [DT23]. Let χ : R − −→ R − , where R − := (−∞, 0], be an increasing function.…”