### Abstract

Let L be the infinitesimal generator of an analytic semigroup on L ^{2}(ℝ^{n}) with suitable upper bounds on its heat kernels. In Auscher, Duong, and McIntosh (2005) and Duong and Yan (2005), a Hardy space H1L (ℝ^{n}) and a BMO_{l}(ℝ^{n}) space associated with the operator L were introduced and studied. In this paper we define a class of Hp/L(ℝ^{n}) spaces associated with the operator L for a range of p < 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 Hp/l(ℝ^{n}) spaces. We then establish a duality theorem between the Hp L(ℝ^{n}) spaces and the Morrey-Campanato spaces in that same paper. As applications, we obtain the boundedness of fractional integrals on Hp/L(ℝ^{n}) and give the inclusion between the classical H ^{p}(ℝ^{n}) spaces and the Hp/L(ℝ^{n}) spaces associated with operators.

Original language | English |
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Pages (from-to) | 4383-4408 |

Number of pages | 26 |

Journal | Transactions of the American Mathematical Society |

Volume | 360 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2008 |