4 votes

On a density property of signed singular measures

Yes, this works. Write $d\mu = s\, d|\mu|$, with $|\mu|$ denoting the total variation of $\mu$ and $s(x)=\pm 1$. We can recover $s(x)$ for $|\mu|$-a.e. $x$ as the derivative $s(x)=\lim_{|I|\to 0} \mu(...
Christian Remling's user avatar
1 vote

Controlling convolutions with maximal functions

For simplicity consider $f \in \mathcal{S}$. Fix $\psi\in C^\infty_c(\mathbb{R}^n,[0,\infty))$ with $\int \psi = 1$. Define $$ \varphi_{\epsilon,y}(x) = \epsilon^{-n}\psi( \epsilon^{-1}(x-y)) $$ so we ...
Willie Wong's user avatar
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