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A note on \(A_p\) weights: Pasting weights and changing variables. (English) Zbl 1045.42015
Summary: For two weights \(u,w\) on \(\mathbb{R}^n\), we show that \(w \in A_{p,u}\) (the Muckenhoupt class of weights) if and only if \(wu\in A_p\) and \(wu^{1-p}\in A_p\), under the assumption that \(u\in A_r\) for every \(r>1\). We also prove a rather general result on pasting weights on \(\mathbb{R}\) that satisfy the \(A_p\) condition.

MSC:
42B25 Maximal functions, Littlewood-Paley theory
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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