Commutators of the Fractional Hardy Operator on Weighted Variable Herz-Morrey Spaces
Amjad Hussain, Muhammad Asim, Muhammad Aslam, Fahd Jarad
Abstract
In the present paper, our aim is to establish the boundedness of commutators of the fractional Hardy operator and its adjoint operator on weighted Herz-Morrey spaces with variable exponents <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mtext>M</a:mtext> <a:msubsup> <a:mrow> <a:mover accent="true"> <a:mtext>K</a:mtext> <a:mo>̇</a:mo> </a:mover> </a:mrow> <a:mrow> <a:mi>p</a:mi> <a:mo>,</a:mo> <a:mi>q</a:mi> <a:mfenced open="(" close=")"> <a:mrow> <a:mo>⋅</a:mo> </a:mrow> </a:mfenced> </a:mrow> <a:mrow> <a:mi>α</a:mi> <a:mfenced open="(" close=")"> <a:mrow> <a:mo>⋅</a:mo> </a:mrow> </a:mfenced> <a:mo>,</a:mo> <a:mi>λ</a:mi> </a:mrow> </a:msubsup> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>w</a:mi> </a:mrow> </a:mfenced> </a:math> .