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arXiv · 1808.05189

Some estimates for the bilinear fractional integrals on the Morrey space

Xiao Yu·Xiangxing Tao·Huihui Zhang·Jianmiao Ruan
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Abstract

In this paper, we are interested in the following bilinear fractional integral operator $B\mathcal{I}_\alpha$ defined by \[ B\mathcal{I}_{\alpha}({f,g})(x)=\int_{% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{n}}\frac{f(x-y)g(x+y)}{|y|^{n-\alpha}}dy, \] with $0< \alpha<n$. We prove the weighted boundedness of $B\mathcal{I}_\alpha$ on the Morrey type spaces. Moreover, an Olsen type inequality for $B\mathcal{I}_\alpha$ is also given.

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Xiao Yu, Xiangxing Tao, Huihui Zhang, Jianmiao Ruan. 2018-08-15. Some estimates for the bilinear fractional integrals on the Morrey space. https://arxiv.org/abs/1808.05189

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