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<p>In this paper, we introduce the concept of general <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> projection body and general <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> centroid body of general measures with positive homogeneity density function, and prove the corresponding extreme inequalities. Meanwhile, we also study their measure comparison problems and monotone inequalities.</p>

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EXTREME INEQUALITIES OF GENERAL \(L_p\) \(\mu\)-PROJECTION BODY AND GENERAL \(L_p\) \(\mu\)-CENTROID BODY

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • C. Li,
  • G. Chen

摘要

In this paper, we introduce the concept of general \(L_p\) L p projection body and general \(L_p\) L p centroid body of general measures with positive homogeneity density function, and prove the corresponding extreme inequalities. Meanwhile, we also study their measure comparison problems and monotone inequalities.