Abstract Let R, ₉ be the jth Bessel–Riesz transform, where n 1, 0, and j=1, , n+1. In this article, we establish a Weyl-type asymptotic for R, ₉, M₅, the commutator of R, ₉ with the multiplication operator M₅, based on building a preliminary result that the endpoint weak Schatten norm of R, ₉, M₅ can be characterized via homogeneous Sobolev norm Ẇ^1, n+1 (R+^n+1) of the symbol f. Specifically, the asymptotic coefficient is equivalent to \|f\|ₖ̇^₁, ₍+₁ (R+^{n+1) }. Our main strategy is to relate Bessel–Riesz commutator to classical Riesz commutator via Schur multipliers, and then to establish the boundedness of Schur multipliers.
Fan et al. (Fri,) studied this question.