The weighted Herz-type Hardy spaces hK
q
α,p
(ω1,ω2) |
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Authors: | Fan Dashan Yang Dachun |
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Institution: | (1) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, 53201 Milwaukee, WI, U.S.A.;(2) Department of Mathematics, Beijing Normal University, 100875 Beijing, The People's Republic of China |
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Abstract: | Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. |
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Keywords: | |
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