Weighted Alpert Wavelets
| Autor: | Brett D. Wick, Eric T. Sawyer, Robert Rahm |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Conjecture
Basis (linear algebra) Lebesgue measure Applied Mathematics General Mathematics Operator (physics) 010102 general mathematics Order (ring theory) 020206 networking & telecommunications math.CA 02 engineering and technology 01 natural sciences Combinatorics Mathematics - Classical Analysis and ODEs Bounded function Classical Analysis and ODEs (math.CA) FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Energy condition 0101 mathematics Borel measure Analysis Mathematics |
| Popis: | In this paper we construct a wavelet basis in weighted L^2 of Euclidean space possessing vanishing moments of a fixed order for a general locally finite positive Borel measure. The approach is based on a clever construction of Alpert in the case of Lebesgue measure that is appropriately modified to handle the general measures considered here. We then use this new wavelet basis to study a two-weight inequality for a general Calder\'on-Zygmund operator on the real line and show that under suitable natural conditions, including a weaker energy condition, the operator is bounded from one weighted L^2 space to another if certain stronger testing conditions hold on polynomials. An example is provided showing that this result is logically different than existing results in the literature. Comment: v2: 26 pages, typos corrected, Theorem changed to a Conjecture |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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