Commutators of n-dimensional rough Hardy operators

Abstract

In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.

Boundedness for a Class of Generalized Commutators of Fractional Hardy Operators with a Rough Kernel

“…By checking [19] carefully, one can draw the conclusion that if one replaces H Ω, ( ) by H |Ω|, | |( ), then (16) still holds. Lemma 7.…”

“…In 2011, Fu et al [19] proved the boundedness of the commutator of fractional Hardy operator with a rough kernel on -Central Morrey space. Later, Fu et al [28] proved the boundness of the weighted Hardy operator and its commutator on -Central Morrey space.…”

Endpoint Estimates for Generalized Commutators of Hardy Operators onH1Space

“…When = 0, we simply denote H 0 by H and H 0 is just the -dimensional Hardy operator proposed by Christ and Grafakos in [4] (without considering the constant ] ). In 2011, Fu et al [6] studied the following -dimensional fractional Hardy operator with a homogeneous kernel:…”

“…where Ω ∈ ( −1 ). Fu et al [6] proved that H Ω, is bounded on Herz type space and -central Morrey space. Here H Ω,…”

Weighted Estimates for Commutators of -Dimensional Rough Hardy Operators

“…In [3], it was proved that the commutators Ω were bounded on the Lebesgue spaces and Herz spaces if ∈ max{ , } (R ). Recently, Gao obtained in [4] that Ω is also bounded from the Morrey-Herz spaceṡ,…”