【摘 要】
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The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with vari
【机 构】
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Department of Mathematics, Yili Normal University, Xinjiang 835000, P.R.China
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The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators.Immediately after,applying the characterizations of TriebelLizorkin space with variable exponent,we obtain that b ∈(A)β if and only if the commutator ofCalderón-Zygmund singular integral operator is bounded,respectively,from Lp(·) (Rn) to (F)β,∞p(·),from Lp(·) (Rn) to Lq(·) (Rn) with 1/p(·)-1/q(·) =β/n.Moreover,we prove that the commutator of Riesz potential operator also has corresponding results.
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