On Carleman's and Knopp's inequalities

• 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

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Mathematics

Matematik

Mathematical analysis

Publication and Content Type

ref (subject category)

art (subject category)