کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6415254 | 1335008 | 2012 | 71 صفحه PDF | دانلود رایگان |
In this paper, the authors first show that the classical Hardy space H1(Rn) can be characterized by the non-tangential maximal functions and the area integrals associated with the semigroups eâtP and eâtP, respectively, where P is an elliptic operator with real constant coefficients of homogeneous order 2m (m⩾1). Moreover, the authors also prove that H1(Rn) can be characterized by the Riesz transforms âmPâ1/2 if and only if m is an odd integer. In the main part of this paper, the authors develop a theory of Hardy space associated with L, where L is a higher order divergence form elliptic operator with complex bounded measurable coefficients. The authors set up a molecular Hardy space HL1(Rn) and give its characterizations by area integrals related to the semigroups eâtL and eâtL, respectively. Finally, authors give the (HL1,L1) boundedness of Riesz transforms, square functions and maximal functions associated with L.
Journal: Journal of Functional Analysis - Volume 263, Issue 3, 1 August 2012, Pages 604-674