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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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