Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces
We prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/929381 |
| Summary: | We prove that b is in Lipβ(ω) if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω) to Lq,kq/p(ω1-(1-α/n)q,ω), where 0<β<1, 0<α+β<n,1<p<n/(α+β), 1/q=1/p-(α+β)/n, 0≤k<p/q, ωq/p∈A1, and rω>(1-k)/(p/(q-k)), and here rω denotes the critical index of ω for the reverse Hölder condition. |
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| ISSN: | 1085-3375 1687-0409 |