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<p>In this study, we discuss several convergence results of fractal measure. We analyze several fundamental convergence theorems pertaining to fractal Lebesgue integrals. Further, we introduce the notion of fractal Lebesgue spaces that consist of fractal Lebesgue integrable functions. The paper also delves into the characteristics of these newly created spaces and highlights essential convergence theorems. Moreover, we investigate the boundedness of the mathematical operator called fractal Laplace operator on fractal Lebesgue spaces.</p>

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Fractal Laplace transform: The boundedness in Fractal Lebesgue spaces

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • Hemanta Kalita,
  • Palle E. T. Jorgensen,
  • Lucas Wangwe,
  • Bipan Hazarika

摘要

In this study, we discuss several convergence results of fractal measure. We analyze several fundamental convergence theorems pertaining to fractal Lebesgue integrals. Further, we introduce the notion of fractal Lebesgue spaces that consist of fractal Lebesgue integrable functions. The paper also delves into the characteristics of these newly created spaces and highlights essential convergence theorems. Moreover, we investigate the boundedness of the mathematical operator called fractal Laplace operator on fractal Lebesgue spaces.