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Let L 1 be a nonnegative self-adjoint operator in L 2(ℝ n ) satisfying the Davies-Gaffney estimates and L 2 a second order divergence form elliptic operator with complex bounded measurable coefficients. A typical example of L 1 is the Schrödinger operator -Δ+V, where Δ is the Laplace operator on ℝ n and 0 ≤ V ∞ L1 loc (ℝn). Let Hp Li(ℝn) be the Hardy space associated to L i for iε{1, 2. In this paper, the authors prove that the Riesz transform D (Li -1/2) is bounded from Hp Li (ℝn) to the classical weak Hardy space WH p (ℝ n ) in the critical case that p=n/(n+1). Recall that it is known that D(Li -1/2) is bounded from Hp Li (ℝn) to the classical Hardy space H p (ℝ n ) when pε(n/(n+1), 1]. © 2011 Revista Matemática Complutense.

Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators