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 L¹ ₋₎₂ (Rᵈ) and, for almost every x Rᵈ, V (x) is a symmetric and nonnegative definite matrix.
Addona et al. (2025) studied this question.