Series expansion for L^p Hardy inequalities

Details Series expansion for L^p Hardy inequalities Series expansion for L^p Hardy inequalities

2003-02-26

arxiv.org/abs/math/0302327v1

Mathematics

Analysis of PDEs

16 pages, to appear in the Indiana Univ. Math. J

Scientific paper

We consider a general class of sharp $L^p$ Hardy inequalities in $\R^N$
involving distance from a surface of general codimension $1\leq k\leq N$. We
show that we can succesively improve them by adding to the right hand side a
lower order term with optimal weight and best constant. This leads to an
infinite series improvement of $L^p$ Hardy inequalities.

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