We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-1, author = {Cornelia Kaiser and Lutz Weis}, title = {Wavelet transform for functions with values in UMD spaces}, journal = {Studia Mathematica}, volume = {187}, year = {2008}, pages = {101-126}, zbl = {1213.42145}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-1} }
Cornelia Kaiser; Lutz Weis. Wavelet transform for functions with values in UMD spaces. Studia Mathematica, Tome 187 (2008) pp. 101-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm186-2-1/