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Licensed Unlicensed Requires Authentication Published by De Gruyter September 1, 2005

Hardy's Inequality in a Variable Exponent Sobolev Space

Petteri Harjulehto, Peter Hst and Mika Koskenoja
From the journal


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.

Received: 2004-06-21
Revised: 2005-04-22
Published Online: 2005-September
Published in Print: 2005-September

Heldermann Verlag

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