## Abstract

Let L_{1} and L_{2} be nonnegative self-adjoint operators acting on L^{2} (X_{1} ) and L^{2} (X_{2} ), respectively, where X_{1} and X_{2} are spaces of homogeneous type. Assume that L_{1} and L_{2} have Gaussian heat kernel bounds. This paper aims to study some equivalent characterizations of the weighted product Hardy spaces H^{p}_{w,L}_{1}_{,L2} (X_{1} × X_{2}) associated to L_{1} and L_{2} , for p ∈ (0, ∞) and the weight w belongs to the product Muckenhoupt class A_{∞}(X_{1} × X_{2}). Our main result is that the spaces H^{p}_{w,L}_{1},_{L2} (X_{1} × X_{2}) introduced via area functions can be equivalently characterized by the Littlewood–Paley g-functions and g^{∗}_{λ}_{1},_{λ2} -functions, as well as the Peetre type maximal functions, without any further assumption beyond the Gaussian upper bounds on the heat kernels of L_{1} and L_{2} . Our results are new even in the unweighted product setting.

Original language | English |
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Pages (from-to) | 91-115 |

Number of pages | 25 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 71 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |