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<p>In this paper, we characterize the supporting functionals and smooth points, give the necessary and sufficiency conditions for the smoothness in Orlicz–Lorentz function and sequence spaces generated by N-function and decreasing weight, equipped with both the Orlicz and Luxemburg norms. By employing measure-preserving transformations, we further derive criteria for a functional <i>f</i> in the dual space to attain its norm at <i>x</i> in Orlicz–Lorentz spaces. Finally, the norm of the characteristic function in the Köthe dual of the Orlicz–Lorentz space is explicitly computed.</p>

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Smoothness in Orlicz–Lorentz spaces

  • 期刊论文

  • 发表日期：

    2025年4月19日

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  • Di Wang,
  • Yongjin Li

摘要

In this paper, we characterize the supporting functionals and smooth points, give the necessary and sufficiency conditions for the smoothness in Orlicz–Lorentz function and sequence spaces generated by N-function and decreasing weight, equipped with both the Orlicz and Luxemburg norms. By employing measure-preserving transformations, we further derive criteria for a functional f in the dual space to attain its norm at x in Orlicz–Lorentz spaces. Finally, the norm of the characteristic function in the Köthe dual of the Orlicz–Lorentz space is explicitly computed.