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Topic: Fractal Sobolev Space
Replies: 3   Last Post: Aug 2, 2011 1:05 AM

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Posts: 10
From: Sweden
Registered: 2/4/08
Fractal Sobolev Space
Posted: Jul 31, 2011 5:30 PM
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For a function that belongs to both L^2 (Lebesguespace) and H^1 (the sobolev space with one derivative), I can prove the following inequality for the fractal sobolev norm Ha of degree a (0<a<1)

| u |Ha <= | u |L2 ^(1-a) * | u |H1 ^ a

by using the Hölder inequality on the Fourier transform representation of the sobolev norm. (simple, if I dont made any trivial mistake)

Q1: Why dont I find this inequality in any books? Is this inequality called anything? Does anyone have a reference of similar inequalities?
Q2: Is this inequality valid on bounded domains?

Any help appreciated!

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