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<p>In his beautiful book <i>Singular Integrals and Differentiability Properties of Functions</i>, E.M. Stein introduces Marcinkiewicz integral as an alternative to the differentiation theorem to illustrate (literally quoting from [<CitationRef CitationID="CR1">1</CitationRef>, Ch.I, Sect.2.3]) “the principle that a general point of a measurable set is almost completely surrounded by other points of the set”. We want to explore the theme summarised by this Stein’s sentence, using the notion of superdensity point.</p>

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Marcinkiewicz integral and superdensity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月5日

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  • Silvano Delladio

摘要

In his beautiful book Singular Integrals and Differentiability Properties of Functions, E.M. Stein introduces Marcinkiewicz integral as an alternative to the differentiation theorem to illustrate (literally quoting from [1, Ch.I, Sect.2.3]) “the principle that a general point of a measurable set is almost completely surrounded by other points of the set”. We want to explore the theme summarised by this Stein’s sentence, using the notion of superdensity point.