Characterization for commutators of n-dimensional fractional Hardy operators

In this paper, it was proved that the commutator generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1 (ℝn) to Lp2 (ℝn) if and only if b is a CṀO(ℝn) function, where 1/p1 − 1/p2 = β/n, 1 < p1 < ∞, 0 ⩽ β < n. Furthermore, the characte...

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Bibliographic Details
Published in:Science China. Mathematics 2007-10, Vol.50 (10), p.1418-1426
Main Authors: Fu, Zun-wei, Liu, Zong-guang, Lu, Shan-zhen, Wang, Hong-bin
Format: Article
Language:English
Subjects:
Commutators
Mathematical functions
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Summary:In this paper, it was proved that the commutator generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from Lp1 (ℝn) to Lp2 (ℝn) if and only if b is a CṀO(ℝn) function, where 1/p1 − 1/p2 = β/n, 1 < p1 < ∞, 0 ⩽ β < n. Furthermore, the characterization of on the homogenous Herz space (ℝn) was obtained.
ISSN:1006-9283
1674-7283
1862-2763
1869-1862
DOI:10.1007/s11425-007-0094-4