Hardy spaces, Campanato spaces and higher order Riesz transforms associated with Bessel operators
Year: 2026
Type: article
Abstract: Let $$\nu = (\nu _1, \ldots , \nu _n) \in (-1/2, \infty )^n$$ ν = ( ν 1 , … , ν n ) ∈ ( - 1 / 2 , ∞ ) n , with $$n \ge 1$$ n ≥ 1 , and let $$\Delta _\nu $$ Δ ν be the multivariate Bessel operator defined by $$ \Delta _{\nu } = -\sum _{j=1}^n\left( \frac{\partial ^2}{\partial x_j^2} - \frac{\nu _j^2 - 1/4}{x_j^2} \right) . $$ 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 $$\Delta _\nu $$ Δ ν . We then study the higher-order Riesz transforms associated with $$\Delta _\nu $$ 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 $$\Delta _\nu $$ Δ ν .
Author: The Anh Bui
Institution: Macquarie University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Funder: Macquarie University
OpenAlex ID: W7148409089