2025/04/15 by The Anh Bui, Bui, The Anh
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.2504.10895
Let ν=(ν1,…,νn)∈ (-1,\vc)n, n≥ 1, and let Lν be a self-adjoint extension of the differential operator Lν:= ∑i=1n [-(∂2)/(∂ xi2) + xi2 + (1)/(xi2)(νi2 - (1)/(4))] on Cc^∞(ℝ+n) as the natural domain. The j-th partial derivative associated with Lν is given by δνj = (∂)/(∂ xj) + xj-(1)/(xj)(νj + \f12), j=1,…, n. In this paper, we investigate the weighted estimates of the higher-order Riesz transforms δνk\mathcal L-|k|/2ν, k∈ \mathbb Nn, where δνk=δνnkn… δν1k1. This completes the description of the boundedness of the higher-order Riesz transforms with the full range ν∈ (-1,\vc)n.