Question

Integrable functions that decay slower than every polynomially integrable function

score 222 · Answer 1 · 2026-04-03 08:44:06

222

Views

Integrable functions that decay slower than every polynomially integrable function

Published on 03 Apr 2026 - 8:44

score 740 · Answer 2 · 2026-03-25 11:21:48

740

Views

Understanding proof when equality holds in Minkowski's inequality

Published on 25 Mar 2026 - 11:21

score 33 · Answer 3 · 2019-11-06 23:02:43

33

Views

Recurence $(1+3^{n+1})x_n - 3^n x_{n-1} - 2\cdot 3^n x_{n+1} = y_n$

Published on 06 Nov 2019 - 23:02

score 575 · Answer 4 · 2019-11-07 09:21:26

575

Views

Does Holder's inequality require finite measure space?

Published on 07 Nov 2019 - 9:21

score 555 · Answer 5 · 2026-03-28 21:44:21

555

Views

Proof that if $f, g \in L^1(\mathbb{R}^n)$ with compact support, then the convolution $f*g$ has compact support

Published on 28 Mar 2026 - 21:44

score 211 · Answer 6 · 2019-11-07 20:39:18

211

Views

$f_n \to f$ a.e and $\|f_n\|_\infty \to \|f\|_\infty$, counterexample/(proof?) to $\|f_n-f\|_\infty \to 0$

Published on 07 Nov 2019 - 20:39

score 32 · Answer 7 · 2026-04-02 02:03:02

32

Views

Is $\left\{ u\in H^{1}\left(\Omega\right)\left|\,a<u\left(x\right) <b\:\text{a.e.}\right.\right\}$ open in $H^1(\Omega)$

Published on 02 Apr 2026 - 2:03

score 43 · Answer 8 · 2019-11-07 22:46:29

43

Views

$(Fx)(t) = f(t)x(t)$ is unitary iff $|f(t)| = 1$ almost everywhere

Published on 07 Nov 2019 - 22:46

score 281 · Answer 9 · 2026-03-26 19:02:50

281

Views

Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

Published on 26 Mar 2026 - 19:02

score 1.6k · Answer 10 · 2019-11-10 03:52:36

1.6k

Views

Convergence in $L^1$ and Boundedness in $L^p$ Implies Convergence in $L^p$

Published on 10 Nov 2019 - 3:52

score 449 · Answer 11 · 2026-02-23 06:38:10

449

Views

Is there an absolutely continuous function $f\in L^2$ for which $f'\not\in L^2$?

Published on 23 Feb 2026 - 6:38

score 115 · Answer 12 · 2026-03-28 17:41:18

115

Views

How can we show this inequality for the operator norm of a Markov kernel acting on $L^p$?

Published on 28 Mar 2026 - 17:41

score 30 · Answer 13 · 2019-11-12 14:26:38

30

Views

Unifrom Convergence in $L^1(\mathbb{R})$

Published on 12 Nov 2019 - 14:26

score 65 · Answer 14 · 2026-03-26 00:53:49

65

Views

Studying the off-diagonal case of this operator $f \mapsto \int_{B(0,1)} f(x-y)dy $

Published on 26 Mar 2026 - 0:53

score 473 · Answer 15 · 2026-03-29 12:04:01

473

Views

Convolution of an $L^p$ function with a Compactly supported continuous function. What does it give?

Published on 29 Mar 2026 - 12:04

List Question

Integrable functions that decay slower than every polynomially integrable function

Understanding proof when equality holds in Minkowski's inequality

Recurence $(1+3^{n+1})x_n - 3^n x_{n-1} - 2\cdot 3^n x_{n+1} = y_n$

Does Holder's inequality require finite measure space?

Proof that if $f, g \in L^1(\mathbb{R}^n)$ with compact support, then the convolution $f*g$ has compact support

$f_n \to f$ a.e and $\|f_n\|_\infty \to \|f\|_\infty$, counterexample/(proof?) to $\|f_n-f\|_\infty \to 0$

Is $\left\{ u\in H^{1}\left(\Omega\right)\left|\,a<u\left(x\right) <b\:\text{a.e.}\right.\right\}$ open in $H^1(\Omega)$

$(Fx)(t) = f(t)x(t)$ is unitary iff $|f(t)| = 1$ almost everywhere

Let $(a_n)\subset\mathbb{C}$ be bounded. Then $T_a\colon\ell^p\to\ell^p, \ (T_a x)_n:=a_n x_n$ compact iff $a_n\to0$.

Convergence in $L^1$ and Boundedness in $L^p$ Implies Convergence in $L^p$

Is there an absolutely continuous function $f\in L^2$ for which $f'\not\in L^2$?

How can we show this inequality for the operator norm of a Markov kernel acting on $L^p$?

Unifrom Convergence in $L^1(\mathbb{R})$

Studying the off-diagonal case of this operator $f \mapsto \int_{B(0,1)} f(x-y)dy $

Convolution of an $L^p$ function with a Compactly supported continuous function. What does it give?

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