Multilinear fractional integral with rough kernel on variable exponent Morrey-Herz spaces

• Main Authors: Afif Abdalmonem, Omer Abdalrhman, Shuangping Tao
• Format: Article
• Language: English
• Published: Ptolemy Scientific Research Press 2019-05-01
• Series: Open Journal of Mathematical Sciences
• Subjects: multilinear fractional integral; rough kernel; bmo function; lipschitz function
• Online Access: https://pisrt.org/psr-press/journals/oms-vol-3-2019/multilinear-fractional-integral-with-rough-kernel-on-variable-exponent-morrey-herz-spaces/

In this article, we study a class of the multilinear fractional integral with rough kernel on Morrey-Herz space with \(p(\cdot), q(\cdot), \alpha(\cdot).\) By using the properties of the variable exponent spaces, the boundedness of the multilinear fractional integral operator is obtained on variable nonhomogeneous Morrey-Herz spaces \({MK}_{q(\cdot),p(\cdot)}^{\alpha(\cdot),\lambda}(\mathbb{R}^{n}).\)