In[6], Hu and Yang obtain a variant sharp estimate for the multilinear singular integral operators. The main purpose of this paper is to prove a sharp inequality for some multilinear operators related to certain non-convolution type integral operators. In fact, we shall establish the sharp inequality for the multilinear operators only under certain conditions on the size of the integral operato...

We introduce the class of variable anisotropic singular integral operators associated to a continuous multi-level ellipsoid cover $$\Theta $$ $$\mathbb {R}^n$$ introduced by Dahmen et al. (Constr Approx 31:149–194, 2010). This is an extension classical isotropic on $${\mathbb R}^n$$ arbitrary smoothness and their analogues for general expansive matrices first author Bownik (Mem Am Math Soc 164(...

Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...