Boundedness of commutators of rough Hardy operators on grand variable Herz spaces
Babar Sultan, Mehvish Sultan
Abstract
Abstract The aim of this paper is to obtain the boundedness of commutators of Hardy operators with rough kernels on grand variable Herz spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msubsup> <m:mover accent="true"> <m:mi>K</m:mi> <m:mo>˙</m:mo> </m:mover> <m:mrow> <m:mi>q</m:mi> <m:mo></m:mo> <m:mrow> <m:mo rspace="4.2pt" stretchy="false">(</m:mo> <m:mo rspace="4.2pt">⋅</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mrow> <m:mi>a</m:mi> <m:mo></m:mo> <m:mrow> <m:mo rspace="4.2pt" stretchy="false">(</m:mo> <m:mo rspace="4.2pt">⋅</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mo>,</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>θ</m:mi> </m:mrow> </m:msubsup> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {\dot{K}^{a(\,\cdot\,),u,\theta}_{q(\,\cdot\,)}(\mathbb{R}^{n})} by applying some properties of variable exponent. Moreover, by using the idea of grand variable Herz–Morrey spaces, we will prove the boundedness of Hardy operators on these spaces.