Angelo Lucia
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Registered User
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PhD student at Universidad Complutense de Madrid.
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Apr 9 |
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Convolution in $\ell_p$ when $0<p<1$ Just one one: should it be "Fubini", not "Funini"? |
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Apr 9 |
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Convolution in $\ell_p$ when $0<p<1$ Looks like the optimal exponent is exactly max$(p,q)$. To see this, consider two strictly positive sequences: $a_n, b_n >0$. Then trivially $$ a*b(n) = \sum_{k\in \mathbb Z} a_{n-k} b_k \ge a_n b_0 ;$$ and similarly $a*b(n) \ge b_n a_0$. Then $a*b(n)$ cannot go to zero faster than the slower between $a$ and $b$. @Davide: if you want, you should post an answer. |
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Apr 3 |
asked | Convolution in $\ell_p$ when $0<p<1$ |
