Hardy's Inequality in a Variable Exponent Sobolev Space

By Petteri Harjulehto, P. Hst, M. Koskenoja. Georgian Mathematical Journal, 2005

76 citations recorded by the source corpus.

Abstract We show that a norm version of Hardy's inequality holds in a variable exponent Sobolev space provided the maximal operator is bounded. Our proof uses recent local versions of the inequality for a fixed exponent. We give an example to show that our assumptions on the exponent are essentially sharp. In the one-dimensional case, we derive a necessary and a sufficient condition for Hardy's inequality to hold.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/26a949df1613a6d9d792b32f7ad42ec95e5f0b64

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In Applied Mathematics

1. Yoshihiro Sawano
2. E. Nakai
3. Mitsuo Izuki
4. Dachun Yang
5. Wen Yuan
6. Ciqiang Zhuo
7. Kwok-Pun Ho
8. Shohei Nakamura

In Computational Theory and Mathematics

1. Yoshihiro Sawano
2. Mitsuo Izuki
3. E. Nakai

Citations in the corpus

• FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, background): “For Hardy type inequalities with variable exponents, see also Harjulehto, Hästö and Koskenoja [64], Hästö [67], Mizuta, Nakai, Ohno and Shimomura [122], etc.”