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Herz-type Hardy spaces on Vilenkin groups and their applications

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Abstract

Let 1<q<∞, 1 - 1/q ⩽a<∞ ,0<p<∞; and G be a locally compact Vilenkin group. The authors first introduce the general Herz-type Hardy spaces\(HK_q^{a,p} (G)\) and\(hK_q^{a,p} (G)\), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces\(HK_q^{a,p} (G)\) of the fractional integral operators and the boundedness on the spaces\(hK_q^{a,p} (G)\) of the pseudo-differential operators of order zero.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201, WI, USA

    Dashan Fan

  2. Department of Mathematics, Beijing Normal University, 100875, Beijing, China

    Dachun Yang

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

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Fan, D., Yang, D. Herz-type Hardy spaces on Vilenkin groups and their applications. Sci. China Ser. A-Math. 43, 481–494 (2000). https://doi.org/10.1007/BF02897140

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