This article defines a new class of norms, called mixed p-norm, based on an observation using Orlicz sum. The corresponding unit ball is called a mixed p-norm ball, which is a generalization of the p-norm ball. Then we discuss several properties of the ball, study the duality relationship of mixed p-norm ball. A Hölder type inequality is proved, which is related to the polar body relationship in convex geometry.

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Mixed p-norm Ball

  • Dafu Yuan,
  • Du Zou

摘要

This article defines a new class of norms, called mixed p-norm, based on an observation using Orlicz sum. The corresponding unit ball is called a mixed p-norm ball, which is a generalization of the p-norm ball. Then we discuss several properties of the ball, study the duality relationship of mixed p-norm ball. A Hölder type inequality is proved, which is related to the polar body relationship in convex geometry.