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In theorem 2.9.2, where we are discussing the Regularity of wavelets. The proof begins by showing the uniform boundedness of the function before the proof of holder inequality in two parts one for small and other for large scale.Now my problem is whether there is arelationship between uniform boundedness and holder continuity as what I have found is that there is no use of showing it uniformly bounded. I have given the link where this problem can be find out.

http://books.google.co.in/books?id=Nxnh48rS9jQC&lpg=PA17&ots=tdMj-kjYKG&dq=continuous%20wavelet%20transform%20ten%20lectures%20on%20wavelets&pg=PA47#v=onepage&q=continuous%20wavelet%20transform%20ten%20lectures%20on%20wavelets&f=false

Andres
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I think uniform boundedness is related to the implication of fubini theorem which is being used in tge proof of holder continuity.

SAMEER
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