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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.
Sarah V. Cook. "Good-λ inequalities for wavelets of compact support." Colloquium Mathematicae 99.1 (2004): 7-18. <http://eudml.org/doc/285206>.
@article{SarahV2004, abstract = {For a wavelet ψ of compact support, we define a square function $S_\{w\}$ and a maximal function NΛ. We then obtain the $L_\{p\}$ equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities.}, author = {Sarah V. Cook}, journal = {Colloquium Mathematicae}, keywords = {wavelets; square function; relative distributional inequality; multiresolution analysis; nontangential maximal function}, language = {eng}, number = {1}, pages = {7-18}, title = {Good-λ inequalities for wavelets of compact support}, url = {http://eudml.org/doc/285206}, volume = {99}, year = {2004}, }
TY - JOUR AU - Sarah V. Cook TI - Good-λ inequalities for wavelets of compact support JO - Colloquium Mathematicae PY - 2004 VL - 99 IS - 1 SP - 7 EP - 18 AB - For a wavelet ψ of compact support, we define a square function $S_{w}$ and a maximal function NΛ. We then obtain the $L_{p}$ equivalence of these functions for 0 < p < ∞. We show this equivalence by using good-λ inequalities. LA - eng KW - wavelets; square function; relative distributional inequality; multiresolution analysis; nontangential maximal function UR - http://eudml.org/doc/285206 ER -