Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents (Q2027123)

The authors prove boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents (see Theorem 2.1). As applications, for \(b=(b_1,\dots, b_m)\) such that every \(b_i\) is in the centeral BMO space with variable exponents, the authors further obtain boundedness of the multilinear Calderón-Zygmund commutator \([\mathfrak{b}, T]\) and \(T_{\mathfrak{b}}\) on the product of central Morrey spaces with variable exponents (see Theorems 3.1 and 3.2), where \[[\mathfrak{b}, T]f(x)= \int_{(\mathbb R^n)^m} K(x, y_1, \dots, y_m)\prod_{i=1}^m (b_i(x)-b_i(y_i)) f_i(y_i)\, dy_1\cdots\, dy_m\] and \[T_{\mathfrak{b}}f(x)=\int_{\mathbb R^n} \prod_{i=1}^m (b_i(x)-b_i(y))K(x,y)f(y)\, dy.\]