A weighted hardy-type inequality for 0 < p < 1 with sharp constant

Hardy-type inequalities with sharp costants for 0 < p < 1 for power weight functions were established in [10], [5]. In this work, we give an extension of these inequalities for general weight functions, prove the existence of extremal functions and write them out explicitly.

Authors
Azzouz N.1 , Burenkov V.I. 2, 3 , Senouci A.4
Publisher
Element D.O.O.
Number of issue
2
Language
English
Pages
787-799
Status
Published
Volume
18
Year
2015
Organizations
  • 1 Department of technology sciences, Faculty of technology, Sidi Belabes, Algeria
  • 2 Department of mathematical analysis, Peoples' Friendship University of Russia, Miklukho Maklai St, Moscow, 117198, Russian Federation
  • 3 Cardiff School of Mathematics, Cardiff University, Senghennydd Rd, Cardiff, CF24 4AG, United Kingdom
  • 4 Department of Mathematics, Ibnou-Khaldoun University, Tiaret, Algeria
Keywords
Hardy operator; Weighted Lp -spaces with 0 < p < 1
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