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<p>In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type spaces in terms of various commutators of parabolic fractional operators with time lag. The key tools to achieve these include establishing the appropriate form in the parabolic setting of the Rubio de Francia iteration algorithm, the Cauchy integral trick, and a modified Fourier series expansion argument adapted to the parabolic geometry. The novelty of these results lies in the fact that we not only introduce a new class of commutators associated with parabolic fractional integral operators with time lag, but also utilize them to provide a characterization of the parabolic BMO-type space in the high-dimensional case.</p>

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Parabolic Extrapolation and Its Applications to Characterizing Parabolic BMO Spaces via Parabolic Fractional Commutators

  • 期刊论文

  • 发表日期：

    2026年1月4日

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  • Mingming Cao,
  • Weiyi Kong,
  • Dachun Yang,
  • Wen Yuan,
  • Chenfeng Zhu

摘要

In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type spaces in terms of various commutators of parabolic fractional operators with time lag. The key tools to achieve these include establishing the appropriate form in the parabolic setting of the Rubio de Francia iteration algorithm, the Cauchy integral trick, and a modified Fourier series expansion argument adapted to the parabolic geometry. The novelty of these results lies in the fact that we not only introduce a new class of commutators associated with parabolic fractional integral operators with time lag, but also utilize them to provide a characterization of the parabolic BMO-type space in the high-dimensional case.