The Commutators of Bochner–Riesz Operators for Hermite Operator.

In this paper, we study the L p -boundedness of the commutator [ b , S R δ (H) ] (f) = b S R δ (H) f - S R δ (H) (b f) of a BMO function b and the Bochner–Riesz means S R δ (H) for Hermite operator H = - Δ + | x | 2 on R n , n ≥ 2 . We show that if δ > δ (q) = n (1 / q - 1 / 2) - 1 / 2 , the commutator [ b , S R δ (H) ] is bounded on L p (R n) whenever q < p < q ′ and 1 ≤ q ≤ 2 n / (n + 2) . [ABSTRACT FROM AUTHOR]