Journal of the Mathematical Society of Japan

Musielak–Orlicz Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus

Xuan Thinh DUONG and Tri Dung TRAN

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Let $X$ be a metric space with doubling measure and $L$ be an operator which satisfies Davies–Gaffney heat kernel estimates and has a bounded $H_\infty$ functional calculus on $L^2(X)$. In this paper, we develop a theory of Musielak–Orlicz Hardy spaces associated to $L$, including a molecular decomposition, square function characterization and duality of Musielak–Orlicz Hardy spaces $H_{L,\omega}(X)$. Finally, we show that $L$ has a bounded holomorphic functional calculus on $H_{L,\omega}(X)$ and the Riesz transform is bounded from $H_{L,\omega}(X)$ to $L^1(\omega)$.

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J. Math. Soc. Japan, Volume 68, Number 1 (2016), 1-30.

First available in Project Euclid: 25 January 2016

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Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 46B70: Interpolation between normed linear spaces [See also 46M35] 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]

Musielak–Orlicz function Musielak–Orlicz Hardy space functional calculus Davies–Gaffney estimate Riesz transform


DUONG, Xuan Thinh; TRAN, Tri Dung. Musielak–Orlicz Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus. J. Math. Soc. Japan 68 (2016), no. 1, 1--30. doi:10.2969/jmsj/06810001.

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