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The weighted Herz-type Hardy spaces hK α,pq (ω1,ω2)

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Approximation Theory and its Applications

Abstract

Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA 1(Rn) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk α,pq (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(Rn), the class of C∞(Rn)-functions with compactly support, is dense inhK α,pq (ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK α,pq (ω1,ω2), of any bounded sequence inhK α,pq (ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, 53201, Milwaukee, WI, U.S.A.

    Fan Dashan

  2. Department of Mathematics, Beijing Normal University, 100875, Beijing, The People's Republic of China

    Yang Dachun

Authors
  1. Fan Dashan
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  2. Yang Dachun
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Correspondence to Fan Dashan.

Additional information

Supported by the NECF and the NECF and the NNSF of China.

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Dashan, F., Dachun, Y. The weighted Herz-type Hardy spaces hK α,pq (ω1,ω2). Approx. Theory & its Appl. 13, 19–41 (1997). https://doi.org/10.1007/BF02836808

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  • DOI: https://doi.org/10.1007/BF02836808

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