Hardy spaces associated to self-adjoint operators on general domains
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Duong, Xuan Thinh [1] ; Li, Ji [1] ; Lee, Ming-Yi [2] ; Lin, Chin-Cheng [2]
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[1] Macquarie University
Macquarie University
Australia
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[2] Department of Mathematics, National Central University, Chung-Li, 320, Taiwan, Republic of China
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 305-330
- Idioma: inglés
- DOI: 10.1007/s13348-022-00387-0
- Texto completo no disponible (Saber más ...)
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Resumen
Let be the space of homogeneous type and be a measurable subset of X which may not satisfy the doubling condition. Let L denote a nonnegative self-adjoint operator on which has a Gaussian upper bound on its heat kernel. The aim of this paper is to introduce a Hardy space associated to L on which provides an appropriate setting to obtain boundedness for certain singular integrals with rough kernels. This then implies boundedness for the rough singular integrals, , from interpolation between the spaces and . As applications, we show the boundedness for the holomorphic functional calculus and spectral multipliers of the operator L from to and on for . 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.
