Satoru Shirai
Abstract
We show that b ∈ BM O( n) if and only if the commutator (b, Iα) of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces L p,ϕ ( n )t oL q,ϕ q/p ( n ), where ϕ is non-decreasing, and 1 <p< ∞ ,0 <α<n and 1/q =1 /p − α/n.
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We show that b ∈ BM O( n) if and only if the commutator (b, Iα) of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces L p,ϕ ( n )t oL q,ϕ q/p ( n ), where ϕ is non-decreasing, and 1 <p< ∞ ,0 <α<n and 1/q =1 /p − α/n.
Key concepts: Commutator, Mathematics, Bounded function, Operator (biology), Multiplication (music), Bounded operator, Pure mathematics, Mathematical analysis