Tagged Questions
3
votes
2answers
147 views
Shifting a function is continuous
I'm slightly puzzled by the following: if $g(t)$ is a function in $L^q(X)$ then we can show that $g(t-x)$ is continuous function of $t$, i.e. for $\varepsilon > 0$ we can find $\delta$ such that ...
1
vote
1answer
347 views
Young's inequality for discrete convolution
Young's inequality for convolution of functions states that for $f\in L^p(\mathbb{R}^d)$ and $g\in L^q(\mathbb{R}^d)$ we have
$$\|f\star g\|_r\le\|f\|_p\|g\|_q$$
for $p$, $q$, $r$ satisfying
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