Hardy’s inequalities and integral operators on Herz-Morrey spaces

Abstract

<jats:title>Abstract</jats:title> <jats:p>We obtain some estimates for the operator norms of the dilation operators on Herz-Morrey spaces. These results give us the Hardy’s inequalities and the mapping properties of the integral operators on Herz-Morrey spaces. As applications of this general result, we have the boundedness of the Hadamard fractional integrals on Herz-Morrey spaces. We also obtain the Hilbert inequality on Herz-Morrey spaces.</jats:p>

The boundedness of commutators of rough p-adic fractional Hardy type operators on Herz-type spaces

“…In Euclidean space R n , Herz spaces and Morrey-Herz spaces were firstly introduced in [14] and [26], respectively. For more recent developments in the said spaces we mention the articles [15,27,39] and the references therein. Also, some operators with rough kernels defined on Euclidian space were recently studied on function spaces; see for example [11,12].…”

Calderón Operator on Local Morrey Spaces with Variable Exponents

“…The reader is referred to [2,18,19] for the history and applications of the Hardy' inequalities. For the Hardy's inequalities on the Hardy type spaces, the Lebesgue spaces with variable exponents and the Herz-Morrey spaces, the reader may consult [31][32][33][34][35][36][37].…”

Boundedness of Some Hilbert–Type Operators on the Weighted Morrey–Herz Spaces

“…Recently, Yee and Ho [10], established a necessary condition for the boundedness of the Hilbert-type operator on the Morrey-Herz spaces when λ = 1. For some related results about the boundedness of Hilbert-type and Hardy-type operators on Morrey-Herz spaces the reader is referred to papers [3]- [7] and [10], as well as to the references cited therein.…”