## Journal of the Mathematical Society of Japan

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

#### Abstract

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 $L^1(\omega)$.

#### Article information

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

Dates
First available in Project Euclid: 25 January 2016

https://projecteuclid.org/euclid.jmsj/1453731532

Digital Object Identifier
doi:10.2969/jmsj/06810001

Mathematical Reviews number (MathSciNet)
MR3454550

Zentralblatt MATH identifier
1344.42017

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1453731532

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