Morse Theory and Floer Homology by Michèle Audin & Mihai Damian

Author:Michèle Audin & Mihai Damian
Language: eng
Format: epub
Publisher: Springer London, London

By applying Hölder’s inequality (and using the number q defined by 2/p+1/q=1), we obtain

Consequently,

and, taking the sum over k∈Z,

We now want to give an upper bound for the last term of this sum. We use the inverse

of D that we defined in Section 8.7.a. Since we have assumed that Y∈W 1,2(R×S 1), we have

Once again to simplify the notation, let Z=DY and let denote the norm on . We then have

This is a convolution of and . We can apply Young’s inequality9 to find

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