For a wavelet ψ of compact support, we define a square function and a maximal function NΛ. We then obtain the equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-2, author = {Sarah V. Cook}, title = {Good-$\lambda$ inequalities for wavelets of compact support}, journal = {Colloquium Mathematicae}, volume = {100}, year = {2004}, pages = {7-18}, zbl = {1056.42026}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-2} }
Sarah V. Cook. Good-λ inequalities for wavelets of compact support. Colloquium Mathematicae, Tome 100 (2004) pp. 7-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-2/