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Proves bounded H-infinity-calculus for vector-valued operators in L2, highlighting Gaussian estimates and elliptic operators.
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded H^∞-calculus in L²( Rᵈ; Cᵐ) admits bounded H^∞-calculus for every p∈ (1,∞). We apply this result to the elliptic operator - div(Q∇)+V, where the potential term V is a matrix-valued function whose entries belong to L¹loc( Rᵈ) and, for almost every x∈ Rᵈ, $V(x)$ is a symmetric and nonnegative definite matrix.
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Addona et al. (2025) studied this question.
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