Weighted multidimensional Hardy type inequalities via Jensen's inequality

• The authors prove that Jenson's inequality implies some sharp weighted multidimensional Hardy type inequalities. In particular, their results unify and further extend several results of this type in the literature including the recent results in [A. Čižmešija, J. E. Pečarić and L. E. Persson, J. Approx. Theory 125 (2003), no. 1, 74--84; MR2016841 (2004i:42017); S. Kaijser et al., Math. Inequal. Appl. 8 (2005), no. 3, 403--417; MR2148234 (2006c:26036); S. Kaijser, L. E. Persson and A. Öberg, J. Approx. Theory 117 (2002), no. 1, 140--151; MR1920123 (2003f:26037)]. The main result is obtained in Theorem 3.1. In Section 4, the authors show that some existing results are special cases of the theorems obtained in this paper.

Subject headings

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

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

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Mathematics

Matematik

MATHEMATICS

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art (subject category)