Notes on boundedness of spectral multipliers on hardy spaces associated to operators

Bui The Anh

doi:10.1215/00277630-1331881

Notes on boundedness of spectral multipliers on hardy spaces associated to operators

Bui The Anh^*

^*Corresponding author for this work

Faculty of Science and Engineering

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let L be a nonnegative self-adjoint operator on L²(X), where X is a space of homogeneous type. Assume that L generates an analytic semigroup e^-tL whose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplier F(L) is bounded on H^p _L(X) for 0 < p ≤ 1, the Hardy space associated to operator L, when F is a suitable function.

Original language	English
Pages (from-to)	109-122
Number of pages	14
Journal	Nagoya Mathematical Journal
Volume	203
DOIs	https://doi.org/10.1215/00277630-1331881
Publication status	Published - Sept 2011

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abstract = "Let L be a nonnegative self-adjoint operator on L2(X), where X is a space of homogeneous type. Assume that L generates an analytic semigroup e-tL whose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplier F(L) is bounded on Hp L(X) for 0 < p ≤ 1, the Hardy space associated to operator L, when F is a suitable function.",

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AB - Let L be a nonnegative self-adjoint operator on L2(X), where X is a space of homogeneous type. Assume that L generates an analytic semigroup e-tL whose kernel satisfies the standard Gaussian upper bounds. We prove that the spectral multiplier F(L) is bounded on Hp L(X) for 0 < p ≤ 1, the Hardy space associated to operator L, when F is a suitable function.

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JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

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Notes on boundedness of spectral multipliers on hardy spaces associated to operators

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