# Hardy spaces associated to self-adjoint operators on general domains

Xuan Thinh Duong, Ming-Yi Lee, Ji Li, Chin Cheng Lin

## 摘要

Let (X, d, μ) be the space of homogeneous type and Ω be a measurable subset of X which may not satisfy the doubling condition. Let L denote a nonnegative self-adjoint operator on L2(Ω) which has a Gaussian upper bound on its heat kernel. The aim of this paper is to introduce a Hardy space HL1(Ω) associated to L on Ω which provides an appropriate setting to obtain HL1(Ω)→L1(Ω) boundedness for certain singular integrals with rough kernels. This then implies Lp boundedness for the rough singular integrals, 1 < p≤ 2 , from interpolation between the spaces L2(Ω) and HL1(Ω). As applications, we show the boundedness for the holomorphic functional calculus and spectral multipliers of the operator L from HL1(Ω) to L1(Ω) and on Lp(Ω) for 1 < p< ∞. We also study the case of the domains with finite measure and the case of the Gaussian upper bound on the semigroup replaced by the weaker assumption of the Davies–Gaffney estimate.

原文 ???core.languages.en_GB??? Collectanea Mathematica https://doi.org/10.1007/s13348-022-00387-0 已被接受 - 2022