Semigroup kernels, Poisson bounds, and holomorphic functional calculus

Xuan T. Duong; Derek W. Robinson

doi:10.1006/jfan.1996.0145

Semigroup kernels, Poisson bounds, and holomorphic functional calculus

Xuan T. Duong^*, Derek W. Robinson

^*Corresponding author for this work

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

126 Citations (Scopus)

Abstract

Let L be the generator of a continuous holomorphic semigroup S whose action is determined by an integral kernel K on a scale of spaces L_p(X; ρ). Under mild geometric assumptions on (X, ρ), we prove that if L has a bounded H_∞-functional calculus on L₂(X; ρ) and K satisfies bounds typical for the Poisson kernel, then L has a bounded H_∞-functional calculus on L_p(X; ρ) for each p ∈.

Original language	English
Pages (from-to)	89-128
Number of pages	40
Journal	Journal of Functional Analysis
Volume	142
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1996.0145
Publication status	Published - 25 Nov 1996

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title = "Semigroup kernels, Poisson bounds, and holomorphic functional calculus",

abstract = "Let L be the generator of a continuous holomorphic semigroup S whose action is determined by an integral kernel K on a scale of spaces Lp(X; ρ). Under mild geometric assumptions on (X, ρ), we prove that if L has a bounded H∞-functional calculus on L2(X; ρ) and K satisfies bounds typical for the Poisson kernel, then L has a bounded H∞-functional calculus on Lp(X; ρ) for each p ∈.",

author = "Duong, {Xuan T.} and Robinson, {Derek W.}",

year = "1996",

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AU - Robinson, Derek W.

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N2 - Let L be the generator of a continuous holomorphic semigroup S whose action is determined by an integral kernel K on a scale of spaces Lp(X; ρ). Under mild geometric assumptions on (X, ρ), we prove that if L has a bounded H∞-functional calculus on L2(X; ρ) and K satisfies bounds typical for the Poisson kernel, then L has a bounded H∞-functional calculus on Lp(X; ρ) for each p ∈.

AB - Let L be the generator of a continuous holomorphic semigroup S whose action is determined by an integral kernel K on a scale of spaces Lp(X; ρ). Under mild geometric assumptions on (X, ρ), we prove that if L has a bounded H∞-functional calculus on L2(X; ρ) and K satisfies bounds typical for the Poisson kernel, then L has a bounded H∞-functional calculus on Lp(X; ρ) for each p ∈.

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DO - 10.1006/jfan.1996.0145

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EP - 128

JO - Journal of Functional Analysis

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Semigroup kernels, Poisson bounds, and holomorphic functional calculus

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