Sentence examples for boundedness for the commutators from inspiring English sources
In [10, 11], the boundedness for the commutators generated by the singular integral operators and the weighted BMO and Lipschitz functions on L p ( R n ) ( 1 < p < ∞ ) spaces are obtained (also see [12, 13]).
In [10, 11], the boundedness for the commutators generated by the singular integral operators and the weighted B M O and Lipschitz functions on L p ( R n ) ( 1 < p < ∞ ) spaces are obtained.
In [5, 8, 9], the boundedness for the commutators generated by the singular integral operators and Lipschitz functions on Triebel-Lizorkin and L p ( R n ) ( 1 < p < ∞ ) spaces are obtained.
In [13, 14], the weighted boundedness for the commutators generated by the singular integral operators and BMO or Lipschitz functions on L p ( R n ) ( 1 < p < ∞ ) spaces are obtained.
In [9 12], the boundedness for the commutators and multilinear operators generated by the singular integral operators and Lipschitz functions on L p ( R n ) ( 1 < p < ∞ ) and Triebel-Lizorkin spaces are obtained.
In [8, 9], the boundedness for the commutators generated by singular integral operators and Lipschitz functions on Triebel-Lizorkin and L p ( R n ) ( 1 < p < ∞ ) spaces is obtained.
Particularly, we should mention the work of Torchinsky and Wang [21], where they established the L p ( R d ) boundedness for the commutator generated by the Marcinkiewicz integral M Ω and BMO ( R d ) function with p ∈ ( 1, ∞ ).
Note that, from the preceding theorem, one cannot deduce (L^{p}(mathbb {R}^{n};v)) boundedness for the commutator operator by taking (lambda=-1/p), just in the case of Theorem 3.3.
