2011/07/26 by Jun Cao, Dachun Yang, Cao, Jun +3
Mathematics · #35J10 (Secondary) #42B25 #42B30 #47B06 (Primary) 42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #math.CA #math.FA #msc:35J10 #msc:42B20 #msc:42B25 #msc:42B30 #msc:47B06
paper · pdf · doi:10.48550/arxiv.1107.5097
Rev. Mat. Complut. (to appear)
openalex publication_date 2011/07/26 · arxiv created 2012/06/28 · arxiv updated 2012/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let L1 be a nonnegative self-adjoint operator in L2(\mathbb Rn) satisfying the Davies-Gaffney estimates and L2 a second order divergence form elliptic operator with complex bounded measurable coefficients. A typical example of L1 is the Schrödinger operator -Δ+V, where Δ is the Laplace operator on \mathbb Rn and 0≤ V∈ L1\mathoploc (\mathbb Rn). Let HpLi(ℝn) be the Hardy space associated to Li for i∈\1, 2\. In this paper, the authors prove that the Riesz transform D (Li-1/2) is bounded from HpLi(ℝn) to the classical weak Hardy space WHp(ℝn) in the critical case that p=n/(n+1). Recall that it is known that D (Li-1/2) is bounded from HpLi(ℝn) to the classical Hardy space Hp(ℝn) when p∈(n/(n+1), 1].