Some estimates of intrinsic square functions on the weighted Herz-type Hardy spaces

Abstract

In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley G-function and G * λ -function on these spaces. MSC: Primary 42B25; secondary 42B30

Commutators of Multilinear Singular Integrals on Weighted Herz Spaces

“…Recently, many authors considered the boundedness of operators and their commutators on weighted Herz spaces. Wang in [13] proved that the intrinsic square functions are bounded on weighted Herz spaces and in [14] he also obtained the boundedness of the intrinsic square functions on weighted Herz type Hardy spaces. In [15], Kuang considered the boundedness of generalized Hausdorff operators on weighted Herz spaces; Hu et al in [16] established the weighted boundedness for the commutator of fractional integral operators on Herz spaces.…”

Weighted Norm Estimates for Commutators of Several Square Functions

“…In 2014, Wang [20] proved that these square functions is bounded from weighted Herz spaces to itself. In 2015, Wang [21] further discussed the boundedness of these square functions on weighted Herz-Hardy spaces. More conclusions of square functions are referred to [1,2,4,11,15,19,24].…”

“…More conclusions of square functions are referred to [1,2,4,11,15,19,24]. Motivated by Wang [21] and Lu [9], it is a natural problem to ask whether commutators of these square functions are bounded from weighted Herz-type Hardy spaces to Herz spaces? In this paper we shall answer this problem affirmatively.…”

Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent

“…Meanwhile, the weak Herz-type Hardy spaces are the suitable local version of the weak Hardy spaces W H p (R n ). The classical weak Herz type spaces and related function spaces have interesting applications in studying boundedness of many operators and the theory of partial differential equations; see, for example [5,10,12,14,16].…”