Details

Autor(en) / Beteiligte

• Yan, Lixin

Titel

Classes of Hardy Spaces Associated with Operators, Duality Theorem and Applications

Ist Teil von

• Transactions of the American Mathematical Society, 2008-08, Vol.360 (8), p.4383-4408

Ort / Verlag

Providence, RI: American Mathematical Society

Erscheinungsjahr

2008

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• Let L be the infinitesimal generator of an analytic semigroup on L²(ℝⁿ) with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space $H_{L}^{1}(ℝ^{n})$ and a $\text{BMO}_{L}(ℝ^{n})$ space associated with the operator L were introduced and studied. In this paper we define a class of $H_{L}^{p}(ℝ^{n})$ spaces associated with the operator L for a range of p &lt 1 acting on certain spaces of Morrey-Campanato functions defined in "New Morrey-Campanato spaces associated with operators and applications" by Duong and Yan (2005), and they generalize the classical $H^{p}(ℝ^{n})$ spaces. We then establish a duality theorem between the $H_{L}^{p}(ℝ^{n})$ spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on $H_{L}^{p}(ℝ^{n})$ and give the inclusion between the classical $H^{p}(ℝ^{n})$ spaces and the $H_{L}^{p}(ℝ^{n})$ spaces associated with operators.