3 papers
math.AP2026
Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space
The Anh Bui, Konstantin Merz
We consider Hardy operators, i.e., homogeneous Schrödinger operators consisting of the ordinary or fractional Laplacian in a half-space plus a potential, which only depends on the…
math.FA2026
Dunkl paraproducts and fractional Leibniz rules for the Dunkl Laplacian
The Anh Bui, Suman Mukherjee
We establish fractional Leibniz rules for the Dunkl Laplacian of the form $$\|(-Î_k)^s(fg)\|_{L^p(dμ_k)} \lesssim \|(-Î_k)^s f\|_{L^{p_1}(dμ_k)} \|g\|_{L^{p_2}(dμ_k)} +…
math.CA2025
Bilinear and Fractional Leibniz Rules Beyond Euclidean Spaces: Weighted Besov and Triebel--Lizorkin Estimates
The Anh Bui
We establish fractional Leibniz rules in weighted settings for nonnegative self-adjoint operators on spaces of homogeneous type. Using a unified method that avoids Fourier transfor…