Abstract
Let(x,d,p)be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition.In this setting,the authors prove that the commutator M(α)b formed by b ∈(RBMO)(μ)and the fractional maximal function M(α)is bounded from Lebesgue spaces Lp(µ)into spaces Lq(μ),where 1/q=1/p-α for α ∈(0,1)and p ∈(1,1/α).Furthermore,the boundedness of the M(α)b on Orlicz spaces LΦ(μ)is established.
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