New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators
Abstract In this paper, we introduce certain classes of multilinear Calderón–Zygmund operators with kernels of Dini’s type. Applying the sharp method and A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ functions, we first establish some weighted norm inequalities for multilinear Calderón–Zygmund ope...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-01-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02560-8 |
| _version_ | 1830299010170093568 |
|---|---|
| author | Yichun Zhao Jiang Zhou |
| author_facet | Yichun Zhao Jiang Zhou |
| author_sort | Yichun Zhao |
| collection | DOAJ |
| description | Abstract In this paper, we introduce certain classes of multilinear Calderón–Zygmund operators with kernels of Dini’s type. Applying the sharp method and A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ functions, we first establish some weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type, including pointwise estimates, strong type, and weak endpoint estimates. Furthermore, similar weighted norm inequalities for commutators with BMO θ ( φ ) $\mathrm{BMO}_{\theta }(\varphi )$ functions are also obtained, but the weak endpoint estimate is of L ( log L ) $L({\mathrm{log}}L)$ type. |
| first_indexed | 2024-12-19T07:59:53Z |
| format | Article |
| id | doaj.art-70998e67337641f89ea192563aca3b4c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-19T07:59:53Z |
| publishDate | 2021-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-70998e67337641f89ea192563aca3b4c2022-12-21T20:29:53ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-01-012021112310.1186/s13660-021-02560-8New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutatorsYichun Zhao0Jiang Zhou1College of Mathematics and System Sciences, Xinjiang UniversityCollege of Mathematics and System Sciences, Xinjiang UniversityAbstract In this paper, we introduce certain classes of multilinear Calderón–Zygmund operators with kernels of Dini’s type. Applying the sharp method and A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ functions, we first establish some weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type, including pointwise estimates, strong type, and weak endpoint estimates. Furthermore, similar weighted norm inequalities for commutators with BMO θ ( φ ) $\mathrm{BMO}_{\theta }(\varphi )$ functions are also obtained, but the weak endpoint estimate is of L ( log L ) $L({\mathrm{log}}L)$ type.https://doi.org/10.1186/s13660-021-02560-8A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ weightBMO θ ( φ ) $\mathrm{BMO}_{\theta }(\varphi )$ functionDini kernelCommutator |
| spellingShingle | Yichun Zhao Jiang Zhou New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators Journal of Inequalities and Applications A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ weight BMO θ ( φ ) $\mathrm{BMO}_{\theta }(\varphi )$ function Dini kernel Commutator |
| title | New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators |
| title_full | New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators |
| title_fullStr | New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators |
| title_full_unstemmed | New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators |
| title_short | New weighted norm inequalities for multilinear Calderón–Zygmund operators with kernels of Dini’s type and their commutators |
| title_sort | new weighted norm inequalities for multilinear calderon zygmund operators with kernels of dini s type and their commutators |
| topic | A p → ∞ ( φ ) $A_{\vec{p}}^{\infty }(\varphi )$ weight BMO θ ( φ ) $\mathrm{BMO}_{\theta }(\varphi )$ function Dini kernel Commutator |
| url | https://doi.org/10.1186/s13660-021-02560-8 |
| work_keys_str_mv | AT yichunzhao newweightednorminequalitiesformultilinearcalderonzygmundoperatorswithkernelsofdinistypeandtheircommutators AT jiangzhou newweightednorminequalitiesformultilinearcalderonzygmundoperatorswithkernelsofdinistypeandtheircommutators |