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Session S38 - Geometric Potential Analysis

Monday, July 19, 20:10 ~ 20:40 UTC-3

Hardy spaces associated to the Kohn Laplacian on a family of model domains in ${\bf C}^2$

Der-Chen Chang

Georgetown University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloaked183cb9be0286c7fc29c0e2293bc974').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyed183cb9be0286c7fc29c0e2293bc974 = 'ch&#97;ng' + '&#64;'; addyed183cb9be0286c7fc29c0e2293bc974 = addyed183cb9be0286c7fc29c0e2293bc974 + 'g&#101;&#111;rg&#101;t&#111;wn' + '&#46;' + '&#101;d&#117;'; var addy_texted183cb9be0286c7fc29c0e2293bc974 = 'ch&#97;ng' + '&#64;' + 'g&#101;&#111;rg&#101;t&#111;wn' + '&#46;' + '&#101;d&#117;';document.getElementById('cloaked183cb9be0286c7fc29c0e2293bc974').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyed183cb9be0286c7fc29c0e2293bc974 + '\'>'+addy_texted183cb9be0286c7fc29c0e2293bc974+'<\/a>';

We establish a Hardy space theory on the boundary of a family of model domains of finite type m via a new discrete square function constructed from the heat kernel. We prove that a class of singular integral operators is not only bounded on the Hardy spaces $H^p(M)$, but also bounded from $H^p(M)$ to $L^p(M)$ for $\frac{m+2}{m+2+\vartheta}$.

Joint work with Yongsheng Han (Auburn University, USA) and Xinfeng Wu (China University of Mining && Technology, China).