Open Access Dissertation
Date of Award
This dissertation consists of two parts:
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.
In part II, We establish a $(p,2)$-atomic decomposition of the Hardy space associated with different homogeneities for $0
Xiao, Yayuan, "Discrete Littlewood-Paley-Stein Theory And Wolff Potentials On Homogeneous Spaces And Multi-Parameter Hardy Spaces" (2013). Wayne State University Dissertations. 811.