A new class of unbalanced haar wavelets that form an unconditional basis for Lp on general measure spaces |
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| Authors: | Maria Girardi Wim Sweldens |
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| Institution: | (1) Department of Mathematics, University of South Carolina, 29208 Columbia, SC;(2) Katholieke Universiteit Leuven, Belgium;(3) Department of Computer Science, Current: Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, 07974 Murray Hill, NJ |
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| Abstract: | Given a complete separable σ-finite measure space (X,Σ, μ) and nested partitions of X, we construct unbalanced Haar-like wavelets on X that form an unconditional basis for Lp (X,Σ, μ) where1<p<∞. Our construction and proofs build upon ideas of Burkholder and Mitrea. We show that if(X,Σ, μ) is not purely atomic, then the unconditional basis constant of our basis is (max(p, q) −1). We derive a fast algorithm to compute the coefficients. |
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| Keywords: | 42C15 60G46 |
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