Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces (Journal of Mathematical Study, 2022)
In this paper, we establish the boundedness of the bilinear fractional integral operator $B_α$ and the subbilinear fractional maximal operator $M_α$ on vanishing generalized Morrey spaces $V_{0}L^{p,φ}(\mathbb{R}^n)$, $V_{∞}L^{p,φ}(\mathbb{R}^n)$ and $V^{(*)}L^{p,φ}(\mathbb{R}^n)$. The main novelty of this article is that we control $B_{α}$ by the subbilinear maximal operator $M$ and $M_{α'}$ with $α'>α$. Some specific examples for the main results of this paper are also included.