Boundedness of the commutators of bilinear operators in new vanishing Morrey spaces
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In this paper, we consider the subspaces of Morrey spaces with respect to certain vanishing properties of functions. In detail, we study the boundedness of the bilinear Hardy-Littlewood maximal commutators, the commutators of the bilinear fractional integral and its corresponding maximal commutators in new vanishing Morrey spaces with the vanishing property $(V_\infty)$ or $(V^*)$, respectively. We also show that the bilinear Calder\'{o}n-Zygmund operators preserve the vanishing properties $(V_0)$ and $(V_{\infty})$. Moreover, similar consequences still hold in the $m$-linear setting.
Abstract
In this paper, we consider the subspaces of Morrey spaces with respect to certain vanishing properties of functions. In detail, we study the boundedness of the bilinear Hardy-Littlewood maximal commutators, the commutators of the bilinear fractional integral and its corresponding maximal commutators in new vanishing Morrey spaces with the vanishing property $(V_\infty)$ or $(V^*)$, respectively. We also show that the bilinear Calder\'{o}n-Zygmund operators preserve the vanishing properties $(V_0)$ and $(V_{\infty})$. Moreover, similar consequences still hold in the $m$-linear setting.