Abstract Let = (₁, , ₙ) (-1/2, ) ⁿ ν = (ν 1, …, ν n) ∈ (- 1 / 2, ∞) n, with n 1 n ≥ 1, and let _ Δ ν be the multivariate Bessel operator defined by = - ₉=₁ⁿ (² xⱼ² - ⱼ² - 1/4xⱼ²). Δ ν = - ∑ j = 1 n ∂ 2 ∂ x j 2 - ν j 2 - 1 / 4 x j 2. In this paper, we develop the theory of Hardy spaces and BMO-type spaces associated with the Bessel operator _ Δ ν. We then study the higher-order Riesz transforms associated with _ Δ ν. First, we show that these transforms are Calderón-Zygmund operators. We further prove that they are bounded on the Hardy spaces and BMO-type spaces associated with _ Δ ν.
The Anh Bui (Wed,) studied this question.
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