Multilinear Fractional Integral Operators with Generalized Kernels

Y Lin, Y Zhao, S Yang - arXiv preprint arXiv:2406.08736, 2024 - arxiv.org
Y Lin, Y Zhao, S Yang
arXiv preprint arXiv:2406.08736, 2024arxiv.org
In this article, we introduce a class of multilinear fractional integral operators with
generalized kernels that are weaker than the Dini kernel condition. We establish the
boundedness of multilinear fractional integral operators with generalized kernels on
weighted Lebesgue spaces and variable exponent Lebesgue spaces, as well as the
boundedness of multilinear commutators generated by multilinear fractional integral
operators with generalized kernels and $ BMO $ functions. Even when the generalized …
In this article, we introduce a class of multilinear fractional integral operators with generalized kernels that are weaker than the Dini kernel condition. We establish the boundedness of multilinear fractional integral operators with generalized kernels on weighted Lebesgue spaces and variable exponent Lebesgue spaces, as well as the boundedness of multilinear commutators generated by multilinear fractional integral operators with generalized kernels and $BMO$ functions. Even when the generalized kernels condition goes back to the Dini kernel condition, the conclusions on the commutators remain new.
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