2 results
MULTIDIMENSIONAL HARDY-TYPE INEQUALITIES VIA CONVEXITY
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 77 / Issue 2 / April 2008
- Published online by Cambridge University Press:
- 01 April 2008, pp. 245-260
- Print publication:
- April 2008
-
- Article
-
- You have access
- Export citation
-
Let an almost everywhere positive function Φ be convex for p>1 and p<0, concave for p∈(0,1), and such that Axp≤Φ(x)≤Bxp holds on
for some positive constants A≤B. In this paper we derive a class of general integral multidimensional Hardy-type inequalities with power weights, whose left-hand sides involve 
instead of 
, while the corresponding right-hand sides remain as in the classical Hardy’s inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.
for some positive constants 
instead of 
, while the corresponding right-hand sides remain as in the classical Hardy’s inequality and have explicit constants in front of integrals. We also prove the related dual inequalities. The relations obtained are new even for the one-dimensional case and they unify and extend several inequalities of Hardy type known in the literature.On Weighted Sobolev Spaces
-
- Journal:
- Canadian Journal of Mathematics / Volume 48 / Issue 3 / 01 June 1996
- Published online by Cambridge University Press:
- 20 November 2018, pp. 527-541
- Print publication:
- 01 June 1996
-
- Article
-
- You have access
- Export citation
