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Results tagged with fa.functional-analysis
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user 68409
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
7
votes
1
answer
493
views
Inequality of the norm of the convolution in $L^p(\mathbb{R}^n)$ with symmetric decreasing r...
Is it true that
$$
||f*g||_p \le ||\,|f|^* * |g|^*||_p\quad ?
$$
where $|f|^*$ and $|g|^*$ are the symmetric decreasing rearrangements of the functions $|f|$ and $|g|$. Under what conditions on $f$ an …
- 193
2
votes
0
answers
82
views
Properties of a Sobolev bound
I am interested in computing
$$
A:=\inf_{f\in L^{2}(\mathbb{R}^3)}\frac{||K^{\frac{1}{4}}f||_2^2}{||f||_{\frac{5}{2}}^2}
$$
where $K:=-\Delta+1$. We call $f_c$ the function that saturates the bound. …
- 193