Open AccessMusielak–Orlicz Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus
Author(s) -
Xuan Thinh Duong,
Tri Dung Tran
Publication year - 2016
Publication title -
journal of the mathematical society of japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.047
H-Index - 36
eISSN - 1881-1167
pISSN - 0025-5645
DOI - 10.2969/jmsj/06810001
Subject(s) - mathematics , holomorphic functional calculus , hardy space , holomorphic function , bounded function , functional calculus , pure mathematics , infinite dimensional holomorphy , calculus (dental) , algebra over a field , finite rank operator , mathematical analysis , lp space , banach space , medicine , eberlein–šmulian theorem , dentistry
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∞ 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 H[L,ω](X). Finally, we show that L has a bounded holomorphic functional calculus on H[L,ω](X) and the Riesz transform is bounded from H[L,ω](X) to L¹(ω).30 page(s