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arXiv 1902.09273math.FA
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加权齐次树上的Hardy空间

Hardy spaces on weighted homogeneous trees

Laura Arditti, Anita Tabacco, Maria Vallarino

摘要:

我们考虑一个无限的齐次树V,它具有定义在图上的通常度量d和一个加权测度μ。度量测度空间V,d,μ)是非加倍的,并且是指数增长性的,因此经典的Hardy空间理论在这种情况下不适用.我们构造了(V,d,μ)上的原子Hardy空间H^1,并研究了它的一些性质,特别是实插值性质和H^1上奇异积分的有界性.

英文摘要:

We consider an infinite homogeneous tree V endowed with the usual metric d defined on graphs and a weighted measure μ. The metric measure space V,d,μ) is nondoubling and of exponential growth, hence the classical theory of Hardy spaces does not apply in this setting. We construct an atomic Hardy space H^1 on (V,d,μ) and investigate some of its properties, focusing in particular on real interpolation properties and on boundedness of singular integrals on H^1.

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