Boundedness of Commutators of a Class of Generalized Calderón-Zygmund Operators on Lebesgue Space with Variable Exponent

Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...

Commutators of Littlewood-Paley Operators on the Generalized Morrey Space

On Boundedness of a Certain Class of Hardy–steklov Type Operators in Lebesgue Spaces

Lp−Lq–boundedness of the map f → w(x) ∫ b(x) a(x) k(x, y)f(y)v(y)dy is described by different types of criteria expressed in terms of given parameters 0 < p, q < ∞, strictly increasing boundaries a(x) and b(x), locally integrable weight functions v, w and a positive continuous kernel k(x, y) satisfying some growth conditions.

Weighted norm inequalities for Toeplitz type operators associated to generalized Calderón–Zygmund operators

Let [Formula: see text] be a generalized Calderón-Zygmund operator or [Formula: see text] ( the identity operator), let [Formula: see text] and [Formula: see text] be the linear operators, and let [Formula: see text]. Denote the Toeplitz type operator by [Formula: see text]where [Formula: see text] and [Formula: see text] is fractional integral operator. In this paper, we establish the sharp ma...

Self-commutators of composition operators with monomial symbols on the Bergman space

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...