Question

Showing $||k_{\lambda} * f - f||_{\infty} \to 0$ as $\lambda \to \infty$

score 53 · Answer 1 · 2026-04-12 09:02:08

53

Views

Showing $||k_{\lambda} * f - f||_{\infty} \to 0$ as $\lambda \to \infty$

Published on 12 Apr 2026 - 9:02

score 286 · Answer 2 · 2026-04-12 21:03:40

286

Views

Extend an integral inequality from $C[0,1]$ to the whole $L^{2}([0,1])$ [related to operator norm].

Published on 12 Apr 2026 - 21:03

score 35 · Answer 3 · 2026-04-12 14:41:53

35

Views

Showing that the $L^p$ norm of a function is greater than a sum

Published on 12 Apr 2026 - 14:41

score 175 · Answer 4 · 2026-04-09 19:07:03

175

Views

Limit of operator norm

Published on 09 Apr 2026 - 19:07

score 138 · Answer 5 · 2026-04-13 21:17:02

138

Views

If $f$ is continuous and $u \in C^0 \cap H^k$, then is it true that $f(u) \in H^{k}$?

Published on 13 Apr 2026 - 21:17

score 52 · Answer 6 · 2026-04-13 18:18:00

52

Views

Prove that the existence of a step function implies the existence of a continuous function in L2

Published on 13 Apr 2026 - 18:18

score 972 · Answer 7 · 2026-04-13 18:14:29

972

Views

Intersection of two $L^p$ spaces is complete.

Published on 13 Apr 2026 - 18:14

score 68 · Answer 8 · 2026-04-13 17:28:11

68

Views

Proving an inclusion map is continuous

Published on 13 Apr 2026 - 17:28

score 76 · Answer 9 · 2026-04-13 21:24:57

76

Views

Extend inequality from dense subset to $H^{1}$

Published on 13 Apr 2026 - 21:24

score 70 · Answer 10 · 2026-04-16 20:53:14

70

Views

Prove theorem similar to Egorov theorem

Published on 16 Apr 2026 - 20:53

score 95 · Answer 11 · 2026-04-10 18:40:52

95

Views

Multiplication operator with fixed continuous function

Published on 10 Apr 2026 - 18:40

score 86 · Answer 12 · 2026-04-14 17:22:07

86

Views

Confused about the relation between $\ell^p$ and $L^p$

Published on 14 Apr 2026 - 17:22

score 309 · Answer 13 · 2026-04-17 01:03:26

309

Views

If $f, g \in L_{loc}^1(\Omega)$ and $\langle f, \phi \rangle=\langle g, \phi \rangle$ for all $\phi \in D(\Omega)$, then $f=g$ a.e. in $\Omega$

Published on 17 Apr 2026 - 1:03

score 73 · Answer 14 · 2026-04-09 08:39:12

73

Views

$C^\infty$ extension operator

Published on 09 Apr 2026 - 8:39

score 73 · Answer 15 · 2026-04-17 13:35:58

73

Views

Can we show $\frac{\nu\left(B_\varepsilon(x)\right)}{\mu\left(B_\varepsilon(x)\right)}\xrightarrow{\varepsilon\to0+}\frac{{\rm d}\nu}{{\rm d}\mu}(x)$?

Published on 17 Apr 2026 - 13:35

List Question

Showing $||k_{\lambda} * f - f||_{\infty} \to 0$ as $\lambda \to \infty$

Extend an integral inequality from $C[0,1]$ to the whole $L^{2}([0,1])$ [related to operator norm].

Showing that the $L^p$ norm of a function is greater than a sum

Limit of operator norm

If $f$ is continuous and $u \in C^0 \cap H^k$, then is it true that $f(u) \in H^{k}$?

Prove that the existence of a step function implies the existence of a continuous function in L2

Intersection of two $L^p$ spaces is complete.

Proving an inclusion map is continuous

Extend inequality from dense subset to $H^{1}$

Prove theorem similar to Egorov theorem

Multiplication operator with fixed continuous function

Confused about the relation between $\ell^p$ and $L^p$

If $f, g \in L_{loc}^1(\Omega)$ and $\langle f, \phi \rangle=\langle g, \phi \rangle$ for all $\phi \in D(\Omega)$, then $f=g$ a.e. in $\Omega$

$C^\infty$ extension operator

Can we show $\frac{\nu\left(B_\varepsilon(x)\right)}{\mu\left(B_\varepsilon(x)\right)}\xrightarrow{\varepsilon\to0+}\frac{{\rm d}\nu}{{\rm d}\mu}(x)$?

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