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 H1 functional calculus on L2(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 HL∞(X). Finally, we show that L has a bounded holomorphic functional calculus on HL∞(X) and the Riesz transform is bounded from HL∞(X) to L1(w).
Original language | English |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 68 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2016 |
Keywords
- Musielak-Orlicz function
- Musielak-Orlicz Hardy space
- Functional calculus
- Davies-Gaffney estimate
- Riesz transform