Lipschitz estimates for commutators of singular integral operators associated with the sections
Abstract Let H be Monge-Ampère singular integral operator, b ∈ L i p F β $b\in Lip_{\mathcal{F}}^{\beta}$ , and 1 / q = 1 / p − β $1/q=1/p-\beta$ . It is proved that the commutator [ b , H ] $[b,H]$ is bounded from L p ( R n , d μ ) $L^{p}(\mathbb{R}^{n},d\mu)$ to L q ( R n , d μ ) $L^{q}(\mathbb{R}...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-017-1299-x |
| Summary: | Abstract Let H be Monge-Ampère singular integral operator, b ∈ L i p F β $b\in Lip_{\mathcal{F}}^{\beta}$ , and 1 / q = 1 / p − β $1/q=1/p-\beta$ . It is proved that the commutator [ b , H ] $[b,H]$ is bounded from L p ( R n , d μ ) $L^{p}(\mathbb{R}^{n},d\mu)$ to L q ( R n , d μ ) $L^{q}(\mathbb{R}^{n},d\mu)$ for 1 < p < 1 / β $1< p<1/\beta$ and from H F p ( R n ) $H^{p}_{\mathcal{F}}(\mathbb{R}^{n})$ to L q ( R n , d μ ) $L^{q}(\mathbb{R}^{n},d\mu)$ for 1 / ( 1 + β ) < p ≤ 1 $1/(1+\beta)< p\leq1$ . For the extreme case p = 1 / ( 1 + β ) $p=1/(1+\beta)$ , a weak estimate is given. |
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| ISSN: | 1029-242X |