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<p>The generalized translation operator is only bounded in Lebesgue spaces with variable exponents if and only if the exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(p(\cdot )\)</EquationSource> </InlineEquation> is constant. In this study, the boundedness of the Riesz Bessel transform generated by the generalized translation operator when the exponent <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p(\cdot )\)</EquationSource> </InlineEquation> is different from a constant is shown in Lebesgue spaces with variable exponent.</p>

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On the boundedness of B-Riesz transform in Lebesgue spaces with variable exponent

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Ismail Ekincioglu,
  • Anıl Burcu Ozyurt Serim

摘要

The generalized translation operator is only bounded in Lebesgue spaces with variable exponents if and only if the exponent \(p(\cdot )\) is constant. In this study, the boundedness of the Riesz Bessel transform generated by the generalized translation operator when the exponent \(p(\cdot )\) is different from a constant is shown in Lebesgue spaces with variable exponent.