Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2602.17031v1</id>\n    <title>Product Hardy Spaces on Spaces of Homogeneous Type: Discrete Product Calderón-Type Reproducing Formula, Atomic Characterization, and Product Calderón--Zygmund Operators</title>\n    <updated>2026-02-19T02:53:48Z</updated>\n    <link href='https://arxiv.org/abs/2602.17031v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2602.17031v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>Let $i\\in\\{1,2\\}$ and $X_i$ be a space of homogeneous type in the sense of Coifman and Weiss with the upper dimension $ω_i$. Also let $η_i$ be the smoothness index of the Auscher--Hytönen wavelet function $ψ^{k_i}_{α_i}$ on $X_i$. In this article, for any $p\\in(\\max\\{\\frac{ω_1}{ω_1+η_1},\\frac{ω_2}{ω_2+η_2}\\}, 1]$, by regarding the product Carleson measure space $\\mathrm{CMO}^p_{L^2}(X_1\\times X_2)$ as the test function space and its dual space $(\\mathrm{CMO}^p_{L^2}(X_1\\times X_2))'$ as the corresponding distribution space, we introduce the product Hardy space $H^p(X_1\\times X_2)$ in terms of wavelet coefficients. Moreover, we establish an atomic characterization of this product Hardy space and, as an application, obtain a criterion for the boundedness of linear operators from product Hardy spaces to corresponding Lebesgue spaces. To escape the wavelet reproducing formula, which is not useful for this atomic characterization because the wavelets have no bounded support, we establish a new discrete product Calderón-type reproducing formula, which holds in the product Hardy space and has bounded support. This reproducing formula also leads to the boundedness of product Calderón--Zygmund operators on the product Hardy space.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='math.FA'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='math.AP'/>\n    <category scheme='http://arxiv.org/schemas/atom' term='math.CA'/>\n    <published>2026-02-19T02:53:48Z</published>\n    <arxiv:comment>72 pages, Submitted</arxiv:comment>\n    <arxiv:primary_category term='math.FA'/>\n    <author>\n      <name>Ziyi He</name>\n    </author>\n    <author>\n      <name>Dachun Yang</name>\n    </author>\n    <author>\n      <name>Taotao Zheng</name>\n    </author>\n  </entry>"
}