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We use iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with \(G-\) type spaces \(g_\alpha ^\alpha (\mathbb R^d_+)\) and \(G_\alpha ^\alpha (\mathbb R^d_+)\) , when \(\alpha > 1\) , and \(\alpha \geq 1\) , respectively. However, in contrast to G-type spaces, Pilipović spaces are nontrivial below the critical index \(\alpha = 1\) .

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On the Iterates of the Laguerre Operator

  • 会议论文

  • 发表日期：

    2025年

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  • Smiljana Jakšić,
  • Stevan Pilipović,
  • Nenad Teofanov,
  • Djordje Vučković

摘要

We use iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with \(G-\) type spaces \(g_\alpha ^\alpha (\mathbb R^d_+)\) and \(G_\alpha ^\alpha (\mathbb R^d_+)\) , when \(\alpha > 1\) , and \(\alpha \geq 1\) , respectively. However, in contrast to G-type spaces, Pilipović spaces are nontrivial below the critical index \(\alpha = 1\) .