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Spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates

Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/146211

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Title: Spectral multipliers for Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
Related: Journal of the Mathematical Society of Japan, Vol. 63, No. 1, (2011), p.295-319
DOI: 10.2969/jmsj/06310295
Publisher: Mathematical Society of Japan
Date: 2011
Author/Creator: Duong, Xuan Thinh
Author/Creator: Yan, Lixin
Description: Let (X,d,μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a non-negative self-adjoint operator on L²(X). Assume that the semigroup e-tL generated by L satisfies the Davies-Gaffney estimates. Let HLp(X) be the Hardy space associated with L. We prove a Hörmander-type spectral multiplier theorem for L on HLp(X) for 0 < p < ∞ the operator m(L) is bounded from HLp(X) to HLp(X) if the function m possesses s derivatives with suitable bounds and s > n(1/p - 1/2) where n is the "dimension" of X. By interpolation, m(L) is bounded on H Lp(X) for all 0 < p < ∞ if m is infinitely differentiable with suitable bounds on its derivatives. We also obtain a spectral multiplier theorem on Lp spaces with appropriate weights in the reverse Hölder class.
Description: 25 page(s)
Subject Keyword: Atom
Subject Keyword: Davies-Gaffney estimate
Subject Keyword: Hardy space
Subject Keyword: Molecule
Subject Keyword: Non-negative self-adjoint operators
Subject Keyword: Space of homogeneous type
Subject Keyword: Spectral multipliers
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

Identifier: http://hdl.handle.net/1959.14/146211
Identifier: ISSN:0025-5645
Identifier: mq_res-ext-2-s2.0-80052171429
Language: eng
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