Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.research

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Ante

Posts: 10
From: Sweden
Registered: 2/4/08
Fractal Sobolev Space
Posted: Jul 31, 2011 5:30 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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!




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.