Boundedness of Multilinear Operators in Herz-type Hardy Space |
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Authors: | Lin Tang Dachun Yang |
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Institution: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China, E-mail: dcyang@bnu.edu.cn, CN |
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Abstract: | Let κ∈ℕ. We prove that the multilinear operators of finite sums of products of singular integrals on ℝn are bounded from HK
α1,p1
q1
(ℝn) ×···×HK
αk,pk
qk
(ℝn) into HK
α,p
q
(ℝn) if they have vanishing moments up to a certain order dictated by the target spaces. These conditions on vanishing moments
satisfied by the multilinear operators are also necessary when αj≥ 0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals
of any orders.
Received September 6, 1999, Revised November 17, 1999, Accepted December 9, 1999 |
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Keywords: | Multilinear operator Calderón-Zygmund operator Fractional integral Multiplier Herz space Hardy space Atom |
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