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<p>In this study, we introduce the weighted modified Morrey spaces when the weight function <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_924_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> belongs to the Muckenhoupt–Wheeden classes and we examined the behavior of the commutator operator through the boundedness of the generalized fractional integral operator and commutator operator through the boundedness of the generalized fractional maximal operator in the weighted modified Morrey spaces by using the appropriate weighted norm inequalities. Our all the weight functions are in the Muckenhoupt–Wheeden classes and the function <i>b</i> belongs to <i>BMO</i> spaces.</p>

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Commutators of the generalized fractional integrals in the weighted modified Morrey spaces

  • 期刊论文

  • 发表日期：

    2025年6月3日

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  • Abdulhamit Kucukaslan

摘要

In this study, we introduce the weighted modified Morrey spaces when the weight function \(\mu\) μ belongs to the Muckenhoupt–Wheeden classes and we examined the behavior of the commutator operator through the boundedness of the generalized fractional integral operator and commutator operator through the boundedness of the generalized fractional maximal operator in the weighted modified Morrey spaces by using the appropriate weighted norm inequalities. Our all the weight functions are in the Muckenhoupt–Wheeden classes and the function b belongs to BMO spaces.