Question

$\lim_{p \to \infty} \|f\|_p = \|f\|_{\infty}$: is convergence monotone when $\mu(X) \leq 1$?

score 546 · Answer 1 · 2016-07-09 05:59:07

546

Views

$\lim_{p \to \infty} \|f\|_p = \|f\|_{\infty}$: is convergence monotone when $\mu(X) \leq 1$?

Published on 09 Jul 2016 - 5:59

score 127 · Answer 2 · 2026-03-30 16:43:29

127

Views

Volterra Operator on Sobolev Space

Published on 30 Mar 2026 - 16:43

score 335 · Answer 3 · 2016-07-11 14:32:11

335

Views

A general version of Gronwall's inequality

Published on 11 Jul 2016 - 14:32

score 952 · Answer 4 · 2026-03-30 16:45:23

952

Views

Convergence of composition of functions in $L^p$

Published on 30 Mar 2026 - 16:45

score 82 · Answer 5 · 2026-03-25 20:36:00

82

Views

How do you rigorously explain the fact that $u \in L^p$ can be non defined over sets of measure 0?

Published on 25 Mar 2026 - 20:36

score 140 · Answer 6 · 2026-03-30 16:48:48

140

Views

$C_c^\infty(\Omega)\subseteq L^p(\Omega)$ for any open $\Omega$?

Published on 30 Mar 2026 - 16:48

score 71 · Answer 7 · 2016-07-14 17:36:08

71

Views

Find all $\alpha$ such that $n^\alpha\chi_{[n,n+1]}$ converges weakly to 0 in $L^p$.

Published on 14 Jul 2016 - 17:36

score 526 · Answer 8 · 2016-07-14 23:14:29

526

Views

How to prove that an $L^2$ function is also an $L^1$ function?

Published on 14 Jul 2016 - 23:14

score 620 · Answer 9 · 2026-03-28 21:51:30

620

Views

L^1 convergence and limsup of convergent sequence

Published on 28 Mar 2026 - 21:51

score 106 · Answer 10 · 2016-07-17 02:52:41

106

Views

For what value $p$ is $l_p$ not a norm or a metric?

Published on 17 Jul 2016 - 2:52

score 161 · Answer 11 · 2016-07-18 23:58:38

161

Views

Let $f$ be a Lebesgue measurable function on $\Bbb{R}$ satisfying some properties, prove $f\equiv 0$ a.e.

Published on 18 Jul 2016 - 23:58

score 61 · Answer 12 · 2016-07-21 02:59:06

61

Views

Compute $\lim_{p\to 1+}\left\|f\right\|_{p}$ where $f\in L^{1}[0,1] \cap L^{2} [0,1]$

Published on 21 Jul 2016 - 2:59

score 56 · Answer 13 · 2016-07-21 18:13:15

56

Views

Bound on $f_h(t) := \frac 1h \int_t^{t+h}f$

Published on 21 Jul 2016 - 18:13

score 24 · Answer 14 · 2016-07-22 09:57:37

24

Views

If $f \in L^p(\epsilon, T)$ for every $\epsilon > 0$, is $f \in L^p(0,T)$?

Published on 22 Jul 2016 - 9:57

score 1.5k · Answer 15 · 2026-03-28 11:26:56

1.5k

Views

Why isn't $\ell^p$ locally convex for $0<p<1$?

Published on 28 Mar 2026 - 11:26

List Question

$\lim_{p \to \infty} \|f\|_p = \|f\|_{\infty}$: is convergence monotone when $\mu(X) \leq 1$?

Volterra Operator on Sobolev Space

A general version of Gronwall's inequality

Convergence of composition of functions in $L^p$

How do you rigorously explain the fact that $u \in L^p$ can be non defined over sets of measure 0?

$C_c^\infty(\Omega)\subseteq L^p(\Omega)$ for any open $\Omega$?

Find all $\alpha$ such that $n^\alpha\chi_{[n,n+1]}$ converges weakly to 0 in $L^p$.

How to prove that an $L^2$ function is also an $L^1$ function?

L^1 convergence and limsup of convergent sequence

For what value $p$ is $l_p$ not a norm or a metric?

Let $f$ be a Lebesgue measurable function on $\Bbb{R}$ satisfying some properties, prove $f\equiv 0$ a.e.

Compute $\lim_{p\to 1+}\left\|f\right\|_{p}$ where $f\in L^{1}[0,1] \cap L^{2} [0,1]$

Bound on $f_h(t) := \frac 1h \int_t^{t+h}f$

If $f \in L^p(\epsilon, T)$ for every $\epsilon > 0$, is $f \in L^p(0,T)$?

Why isn't $\ell^p$ locally convex for $0<p<1$?

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