Commutator Theorems for Fractional Integral Operators on Weighted Morrey Spaces
Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/413716 |
| Summary: | Let L be the infinitesimal generator of an analytic semigroup on L2(Rn) with Gaussian kernel bounds, and let L-α/2 be the fractional integrals of L for 0<α<n. For any locally integrable function b, the commutators associated with L-α/2 are defined by [b,L-α/2](f)(x)=b(x)L-α/2(f)(x)-L-α/2(bf)(x). When b∈BMO(ω) (weighted BMO space) or b∈BMO, the authors obtain the necessary and sufficient conditions for the boundedness of [b,L-α/2] on weighted Morrey spaces, respectively. |
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| ISSN: | 1085-3375 1687-0409 |