Discrete Littlewood-Paley-Stein Theory And Wolff Potentials On Homogeneous Spaces And Multi-Parameter Hardy Spaces

<p>This dissertation consists of two parts:</p> <p>In part I, We establish a new atomic decomposition of the multi-parameter Hardy spaces of homogeneous type and obtain the associated H^p-L^p and H^p-H^p boundedness criterions for singular integral operators. On the other hand, we compare the Wolff and Riesz potentials on spaces of homogenous type, followed by a Hardy-Littlewood-Sobolev type inequality. Then we drive integrability estimates of positive solutions to the Lane-Emden type integral systems on spaces of homogeneous type.</p> <p>In part II, We establish a $(p,2)$-atomic decomposition of the Hardy space associated with different homogeneities for $0<p\le 1$. In addition, We characterize the dual spaces of the weighted multi-parameter Hardy spaces associated with Zygmund dilations, i. e. (H^p_{\mathcal Z}(w))^*=CMO^p_{\mathcal Z}(w) for w\in A_\infty(\mathcal Z) and $0<p\le 1$.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2013

Author dc:creator

• Xiao, Yayuan

Contributors dc:contributor

• Guozhen Lu

• Atomic decomposition
• Discrete Littlewood-Paley-Stein theory
• Hardy space
• Multi-parameter
• Wolff potential
• Zygmund dilation
• Mathematics

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/811

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-1810