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<p>In the present paper we characterize the removable sets for solutions of the fractional heat equation satisfying some parabolic BMO or <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text {Lip}_\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>Lip</mtext> <mi>α</mi> </msub> </math></EquationSource> </InlineEquation> normalization conditions. We do this by introducing associated fractional caloric capacities, that we show to be comparable to a certain parabolic Hausdorff content.</p>

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On fractional parabolic BMO and \(\text {Lip}_{\alpha }\) caloric capacities

  • 期刊论文

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  • 发表日期：

    2025年11月11日

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  • Joan Hernández,
  • Joan Mateu,
  • Laura Prat

摘要

In the present paper we characterize the removable sets for solutions of the fractional heat equation satisfying some parabolic BMO or \(\text {Lip}_\alpha \) Lip α normalization conditions. We do this by introducing associated fractional caloric capacities, that we show to be comparable to a certain parabolic Hausdorff content.