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New properties of the multivariable H^∞ functional calculus of sectorial operators [article]

Olivier Arrigoni, Christian Le Merdy
<span title="2021-04-16">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>

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<span title="2020-07-09">2020</span> <span class="release-stage" >pre-print</span> <span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.04580v1">arXiv:2007.04580v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xkdrt4nxfvcy7biteapwy5z6yq">fatcat:xkdrt4nxfvcy7biteapwy5z6yq</a> </span>
This paper is devoted to the multivariable H^∞ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if (A_1,..., A_d) is such a family, if A_k is R-sectorial of R-type ω_k∈(0,π), k=1,...,d, and if (A_1,..., A_d) admits a bounded H^∞(Σ_θ_1×⋯×Σ_θ_d) joint functional calculus for some θ_k∈ (ω_k,π), then it admits a bounded H^∞(Σ_θ_1×⋯×Σ_θ_d) joint functional calculus for all θ_k∈ (ω_k,π), k=1,...,d. Second we introduce square
more &raquo; ... tions adapted to the multivariable case and extend to this setting some of the well-known one-variable results relating the boundedness of H^∞ functional calculus to square function estimates. Third, on K-convex reflexive spaces, we establish sharp dilation properties for d-tuples (A_1,..., A_d) which admit a bounded H^∞(Σ_θ_1×⋯×Σ_θ_d) joint functional calculus for some θ_k<π/2.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.04580v2">arXiv:2007.04580v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nozf5576w5b23g6d2mzfpq4b7q">fatcat:nozf5576w5b23g6d2mzfpq4b7q</a> </span>
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Citation

Olivier Arrigoni, Christian Le Merdy. "New properties of the multivariable H^∞ functional calculus of sectorial operators." arXiv (2021)