In this paper, the authors establish the sharp maximal estimates for the multilinear iterated commutators generated by [Formula: see text] functions and multilinear singular integral operators with generalized kernels. As applications, the boundedness of this kind of multilinear iterated commutators on the product of weighted Lebesgue spaces and the product of variable exponent Lebesgue spaces ...

Present work contains a method to obtain Jackson and Stechkin type inequalities of approximation by integral functions finite degree (IFFD) in some variable exponent Lebesgue space real defined on $\boldsymbol{R}:=\left( -\infty ,+\infty \right) $. To do this, we employ transference theorem which produce norm starting from $\mathcal{C}(\boldsymbol{R})$, the class bounded uniformly continuous $\...