Commutators of the Bilinear Hardy Operator on Herz Type Spaces with Variable Exponents

Abstract

In this paper, we obtain the boundedness of bilinear commutators generated by the bilinear Hardy operator and BMO functions on products of Herz spaces and Herz-Morrey spaces with variable exponents.

Boundedness of commutators on herz-morry-hardy spaces with variable exponent

“…By the L p(•) (R n ), L p(•) (R n ) -boundedness of the T b Ω (see [13]) and following the same way as we estimated E 1 in Theorem 13, we get E 1 ≤ C b * Υ. Now, we estimate E 2 .…”

“…For G 1 , by the boundedness of the commutator T b Ω in L p(•) (R n ) (see [13]), and following the same way as we estimated G 1 in Theorem 13, we get…”

“…Motivated by [11][12][13], our main purpose of this paper is to study some boundedness for commutators of Calderón−Zygmund operators on Herz-Morrey-Hardy space with two variable exponents. The main tools are properties of variable exponent, BMO function and Lipschitz function.…”