Abstract
In this paper, we study the necessary and sufficient conditions on the parameters for the boundedness of the multilinear fractional maximal operator $\mathcal{M}_{\Omega,\alpha}$ and the multilinear fractional integral operator $\mathcal{I}_{\Omega,\alpha}$ with rough kernels on Morrey spaces and modified Morrey spaces, respectively. This extends some recent results of Guliyev, Hasnov and Zeren; the necessary and sufficient conditions for the boundedness of $M_{\alpha}$ and $I_{\alpha}$ on modified spaces are considered.
Highlights
Kenig and Stein [ ] studied the boundedness of multilinear fractional integral operator Iα,m, < α < mn, on Lebesgue spaces
We study the necessary and sufficient conditions on the parameters for boundedness of the multilinear fractional maximal operator M,α and the multilinear fractional integrals I,α with rough kernels on Morrey spaces and modified Morrey spaces, respectively, whose definitions are given below
(ii) If p =, the condition – /q = α/(n – λ) is necessary and sufficient for the boundedness of the operator Iα from L,λ(Rn) to WLq,λ(Rn). Motivated by these two results above, we study the necessary and sufficient conditions on the parameters for the boundedness of the multilinear fractional maximal operator M,α and the multilinear fractional integral operator I,α with rough kernels on Morrey spaces and modified Morrey spaces, respectively
Summary
Kenig and Stein [ ] studied the boundedness of multilinear fractional integral operator Iα,m, < α < mn, on Lebesgue spaces. We study the necessary and sufficient conditions on the parameters for boundedness of the multilinear fractional maximal operator M ,α and the multilinear fractional integrals I ,α with rough kernels on Morrey spaces and modified Morrey spaces, respectively, whose definitions are given below. (ii) If p = , the condition – /q = α/(n – λ) is necessary and sufficient for the boundedness of the operator Iα from L ,λ(Rn) to WLq,λ(Rn) Motivated by these two results above, we study the necessary and sufficient conditions on the parameters for the boundedness of the multilinear fractional maximal operator M ,α and the multilinear fractional integral operator I ,α with rough kernels on Morrey spaces and modified Morrey spaces, respectively. Since each pj > s , by the Hölder inequality and Lemma . and Lemma . , we have
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
