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<p>The analysis of Morrey spaces, generalized Morrey spaces and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textit{BMO}_\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="italic">BMO</mi> <mi>ϕ</mi> </msub> </math></EquationSource> </InlineEquation> spaces related to the Dunkl operators on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation> are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation> in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation> in Dunkl-type <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\textit{BMO}_\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="italic">BMO</mi> <mi>ϕ</mi> </msub> </math></EquationSource> </InlineEquation> spaces.</p>

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Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and \(BMO_\phi \) spaces associated with Dunkl operator on the real line

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Sumit Parashar,
  • Saswata Adhikari

摘要

The analysis of Morrey spaces, generalized Morrey spaces and \(\textit{BMO}_\phi \) BMO ϕ spaces related to the Dunkl operators on \(\mathbb {R}\) R are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on \(\mathbb {R}\) R in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on \(\mathbb {R}\) R in Dunkl-type \(\textit{BMO}_\phi \) BMO ϕ spaces.