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20232026
most citedEquivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space

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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…

math.FA2025

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 $$\|(-Δ_k)^s(fg)\|_{L^p(dμ_k)} \lesssim \|(-Δ_k)^s f\|_{L^{p_1}(dμ_k)} \|g\|_{L^{p_2}(dμ_k)} + \|f\|…