Bilinear and Fractional Leibniz Rules Beyond Euclidean Spaces: Weighted Besov and Triebel Lizorkin Estimates

This talk presents new fractional Leibniz rules in weighted settings for nonnegative self-adjoint operators on spaces of homogeneous type. The unified approach, which avoids Fourier transform techniques, establishes bilinear estimates for spectral multipliers on weighted Hardy, Besov, and Triebel–Lizorkin spaces. The framework extends beyond Euclidean contexts, encompassing examples such as nilpotent Lie groups, Grushin operators, and Hermite expansions.