Abstract
Let , , and denote the Marcinkiewicz integral, the parameterized area integral, and the parameterized Littlewood-Paley function, respectively. In this paper, the authors give a characterization of BMO space by the boundedness of the commutators of , , and on the generalized Morrey space .
Highlights
Let Sn−1 {x ∈ Rn : |x| 1} be the unit sphere in Rn equipped with the Lebesgue measure dσ
A Ω is the homogeneous function of degree zero on Rn \ {0}, that is, Ω μx Ω x, for any μ > 0, x ∈ Rn \ {0}
The purpose of this paper is to give a characterization of BMO space by the boundedness of the commutators of μΩ, μS, and μ∗λ, on the generalized Morrey space Lp,φ Rn
Summary
Let Sn−1 {x ∈ Rn : |x| 1} be the unit sphere in Rn equipped with the Lebesgue measure dσ. Suppose that Ω satisfies the following conditions. The purpose of this paper is to give a characterization of BMO space by the boundedness of the commutators of μΩ, μS , and μ∗λ, on the generalized Morrey space Lp,φ Rn . C1 log 2/ x − y γ , C1 > 0, γ > 1, x , y ∈ Sn−1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
