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Some characterizations of weighted Herz-type Hardy spaces and their applications

Authors:	Lu Shanzhen Yang Dachun

Institution:	(1) Department of Mathematics, Beijing Normal University, 100875 Beijing, China

Abstract:	In this paper, the authors first establish some new real-variable characterizations of Herz-type Hardy spaces $H \mathop {K _q^{\alpha ,p} }\limits^ \bullet (\omega _1 ;\omega _2 )$ and $H K_q^{\alpha ,p} (\omega _1 ;\omega _2 )$ , where ω₁,ω₃ ∈ A₁-weight, 1<q>∞,n(1−1/q)≤α<∞ and 0<p<∞. Then, using these new characterizations, they investigate the convergence of a bounded set in these spaces, and study the boundedness of some potential operators on these spaces. Supported by the NNSF of China

Keywords:	Herz space Herz-type Hardy space Potential operator
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