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<p>The paper continues the study of Hadamard–Bergman type operators in weighted Lebesgue and Bergman spaces on the unit disc, and considers the case of specific canonical weights with different exponents. We prove sufficient and necessary conditions for boundedness of Hadamard–Bergman and variable Hadamard–Bergman operators between weighted Lebesgue and Bergman type spaces with different weight exponents. We also provide conditions for the boundedness of the same operators between the corresponding weighted Bergman spaces.</p>

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Hadamard–Bergman type operators in weighted Lebesgue and Bergman spaces

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Alexey Karapetyants,
  • Fernando Leon-Saavedra,
  • Evelyn Morales

摘要

The paper continues the study of Hadamard–Bergman type operators in weighted Lebesgue and Bergman spaces on the unit disc, and considers the case of specific canonical weights with different exponents. We prove sufficient and necessary conditions for boundedness of Hadamard–Bergman and variable Hadamard–Bergman operators between weighted Lebesgue and Bergman type spaces with different weight exponents. We also provide conditions for the boundedness of the same operators between the corresponding weighted Bergman spaces.