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Jan
31
awarded  Popular Question
Jan
30
comment Find the sequences $a_n$, such that $\sum_{n=1}^\infty\frac{1}{n^{2/(2-a_n)}}<\infty$.
That's a good idea. Let me see if I can get somewhere with it. Thank you @Alex
Jan
30
comment Find the sequences $a_n$, such that $\sum_{n=1}^\infty\frac{1}{n^{2/(2-a_n)}}<\infty$.
Sorry @Alex, I have fixed it. Thank you.
Jan
30
revised Find the sequences $a_n$, such that $\sum_{n=1}^\infty\frac{1}{n^{2/(2-a_n)}}<\infty$.
added 6 characters in body
Jan
30
asked Find the sequences $a_n$, such that $\sum_{n=1}^\infty\frac{1}{n^{2/(2-a_n)}}<\infty$.
Jan
29
comment Convergence of the series $\sum_{k=1}^{\infty} \frac{1}{2^k} |x-y_k|^{-\alpha}$
Choose $\alpha$ such that the derivative of $|x-x_k|^{-\alpha}$ is in $L^1$ and use any tool like the Monotone Convergence Theorem.
Jan
26
comment Existence of a solution to the poisson equation with a Radon measure on the right hand side.
What is a solution for you in this context?
Jan
25
comment Existence of $u\in C^1[0,1]$ such that $u\notin H^1(0,1)$
What is your definition for $C^1[0,1]$?
Jan
14
awarded  Notable Question
Jan
11
asked Is the Lebesgue $\sigma$-algebra the largest one where $\mu^\star$ is $\sigma$-additive?
Dec
23
answered the relationship between $W^{k,p}(\Omega)$ and $W^{k,p}_0(\Omega)$
Dec
18
answered Sobolev embedding into $L^\infty$
Dec
13
comment Example of signed measure negative
Hint: Take any integrable function $f:\mathbb{R}\to \mathbb{R}$ and consider the measure $\mu(E)=\int_E fd\mu$.
Dec
13
comment Fréchet differentiability of Nemyckij operator defined on $L^2$
You can find the proof of your statement and also learn a lot of things, with respect to Nemyckij operators , in the book: Integral operators in spaces of summable functions, from Krasnosel'skii et al. Amazon link.
Dec
5
awarded  Enlightened
Dec
5
awarded  Nice Answer
Nov
7
comment Does the Orlicz Norm always make the corresponding integral 1?
Yes, this is true. Can you prove that the function $f(t)=\int \Psi(|f|/t)$ is continuous?
Oct
31
awarded  Popular Question
Oct
16
accepted Minimizing continuous, convex and coercive functions in non-reflexive Banach spaces
Oct
15
awarded  Popular Question