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In this paper, we introduce the concept of some weighted operators \(T_{\lambda ,\varphi }\) and \(T_{\lambda ,\omega }\) on weighted Hardy spaces \(H^2_\beta \) . After that we investigate the boundedness of those operators on \(H^2_\beta \) . Finally, we investigate the Hyers-Ulam stability for weighted backward shift operator on \(H^2_\beta \) and by using example, we show that it stable or not stable in which conditions.

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The Boundedness and HU-Stabilities for Some Weighted Operators

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  • 发表日期：

    2026年

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  • Vahid Keshavarz,
  • Zohreh Kefayati,
  • Thabet Abdeljawad

摘要

In this paper, we introduce the concept of some weighted operators \(T_{\lambda ,\varphi }\) and \(T_{\lambda ,\omega }\) on weighted Hardy spaces \(H^2_\beta \) . After that we investigate the boundedness of those operators on \(H^2_\beta \) . Finally, we investigate the Hyers-Ulam stability for weighted backward shift operator on \(H^2_\beta \) and by using example, we show that it stable or not stable in which conditions.