On Carleman and Knopp's Inequalities

نویسندگان

  • Sten Kaijser
  • Lars-Erik Persson
  • Anders Öberg
چکیده

A sharpened version of Carleman’s inequality is proved. This result unifies and generalizes some recent results of this type. Also the “ordinary” sum that serves as the upper bound is replaced by the corresponding Cesaro sum. Moreover, a Carleman type inequality with a more general measure is proved and this result may also be seen as a generalization of a continuous variant of Carleman’s inequality, which is usually referred to as Knopp’s inequality. A new elementary proof of (Carleman–)Knopp’s inequality and a new inequality of Hardy–Knopp type is pointed out.

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عنوان ژورنال:
  • Journal of Approximation Theory

دوره 117  شماره 

صفحات  -

تاریخ انتشار 2002