Abstract
Compactness of the commutators of intrinsic square functions on weighted Lebesgue spaces
Highlights
For ∫ < α ≤ 1, letCα be the family of functions φ : Rn →R such that φ ’s support is contained in {x |x|
In [17], Wang obtained the boundedness of these commutators on weighted Lebesgue space
The first paper on the compactness of commutators was written by Uchiyama [15]. He improved the boundedness result of the commutators of singular integral operators to compactness when the symbol is in CMO
Summary
In [17], Wang obtained the boundedness of these commutators on weighted Lebesgue space We are interested in the compactness for the commutators of Gα , gα , and gλ∗,α on the weighted Lebesgue spaces. The first paper on the compactness of commutators was written by Uchiyama [15] He improved the boundedness result of the commutators of singular integral operators to compactness when the symbol is in CMO. The compactness of the commutator of singular integral operators on weighted spaces was not known until the work of Clop and Cruz [9]. We will show that the commutators of the intrinsic square functions are compact on the weighted Lebesgue spaces when the symbol is in CMO.
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