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Ante
Posts:
10
From:
Sweden
Registered:
2/4/08


Fractal Sobolev Space
Posted:
Jul 31, 2011 5:30 PM


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 ^(1a) *  u H1 ^ a
by using the HÃ¶lder 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!



