The Boundedness of Intrinsic Square Functions on the Weighted Herz Spaces

Abstract

In this paper, we will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and g * λ -function on the weighted Herz spacesK α,p q (w1, w2) (K α,p q (w1, w2)) with general weights. MSC(2010): 42B25; 42B35

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.…”

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

“…Then there exists a constant C > 0 independent of f such that [14], Lerner obtained sharp L p w norm inequalities for the intrinsic square functions in terms of the A p characteristic constant of w for all 1 < p < ∞. For further discussions about the boundedness of intrinsic square functions on various function spaces, we refer the readers to [10,[33][34][35][36][37].…”

Parametric Marcinkiewicz integrals on weighted Herz Spaces

“…Hu , He and Wang [19] studied the boundedness of commutators of fractional integrals in generalized Herz spaces. More results concerning the boundedness of operators on Herz spaces can be seen in [12,17].…”