Question

If $f_n \to f$ in $L^p$ where $|f| \le C$ then we have $-C \vee f_n \wedge C \to f$ in $L^p$

score 35 · Answer 1 · 2020-07-27 08:48:54

35

Views

If $f_n \to f$ in $L^p$ where $|f| \le C$ then we have $-C \vee f_n \wedge C \to f$ in $L^p$

Published on 27 Jul 2020 - 8:48

score 62 · Answer 2 · 2026-02-24 21:34:55

62

Views

$L^p$-norm diverges for a sequence of functions

Published on 24 Feb 2026 - 21:34

score 48 · Answer 3 · 2020-07-27 18:12:27

48

Views

For which $p$ do the following functions converge in $L^p([0,\infty),leb)$?

Published on 27 Jul 2020 - 18:12

score 413 · Answer 4 · 2026-03-31 10:37:57

413

Views

How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Published on 31 Mar 2026 - 10:37

score 34 · Answer 5 · 2020-07-29 22:42:32

34

Views

Convergence in $L^{2}$ implying a convergence $a.e.$

Published on 29 Jul 2020 - 22:42

score 183 · Answer 6 · 2020-07-30 13:13:43

183

Views

Prove that $L^1\cap L^{\infty }\subseteq L^p$ for all $p\in [1,\infty]$

Published on 30 Jul 2020 - 13:13

score 87 · Answer 7 · 2026-04-03 12:54:29

87

Views

Why does $ \frac{1 + |u|^p}{1 + |u|} \in L^{N/2}_{loc}(\Omega) $?

Published on 03 Apr 2026 - 12:54

score 223 · Answer 8 · 2016-07-05 18:44:30

223

Views

If the limit of a $L^2$ sequence is in $L^\infty$, is the sequence bounded in $L^\infty$?

Published on 05 Jul 2016 - 18:44

score 26 · Answer 9 · 2016-07-06 09:49:29

26

Views

Is this sequence uniformly bounded in $L^\infty(\Omega)$?

Published on 06 Jul 2016 - 9:49

score 704 · Answer 10 · 2026-03-30 16:41:41

704

Views

Convolution is continuous

Published on 30 Mar 2026 - 16:41

score 630 · Answer 11 · 2026-03-30 16:48:38

630

Views

How to show that a Schwartz distribution is in a Lebesgue or Sobolev space?

Published on 30 Mar 2026 - 16:48

score 4.4k · Answer 12 · 2026-03-30 16:48:17

4.4k

Views

The convolution of two functions is L1

Published on 30 Mar 2026 - 16:48

score 47 · Answer 13 · 2016-07-07 14:32:13

How can we show that $\int_{|\alpha |\leq N}\hat f(\alpha )e^{2i\pi x\alpha }d\alpha $ converges to $f$ in $L^p(\mathbb R)$ for $1<p\leq 2$.

score 304 · Answer 14 · 2026-03-26 01:07:41

304

Views

Gradient of the solution for Poisson equation

Published on 26 Mar 2026 - 1:07

score 58 · Answer 15 · 2016-07-09 05:42:44

58

Views

For which $p$ is $\frac{1}{x^a+x^b}$ in $\cal{L}^p$?

Published on 09 Jul 2016 - 5:42

List Question

If $f_n \to f$ in $L^p$ where $|f| \le C$ then we have $-C \vee f_n \wedge C \to f$ in $L^p$

$L^p$-norm diverges for a sequence of functions

For which $p$ do the following functions converge in $L^p([0,\infty),leb)$?

How to prove that $|f|\leqslant\|f\|_\infty$ almost everywhere?

Convergence in $L^{2}$ implying a convergence $a.e.$

Prove that $L^1\cap L^{\infty }\subseteq L^p$ for all $p\in [1,\infty]$

Why does $ \frac{1 + |u|^p}{1 + |u|} \in L^{N/2}_{loc}(\Omega) $?

If the limit of a $L^2$ sequence is in $L^\infty$, is the sequence bounded in $L^\infty$?

Is this sequence uniformly bounded in $L^\infty(\Omega)$?

Convolution is continuous

How to show that a Schwartz distribution is in a Lebesgue or Sobolev space?

The convolution of two functions is L1

How can we show that $\int_{|\alpha |\leq N}\hat f(\alpha )e^{2i\pi x\alpha }d\alpha $ converges to $f$ in $L^p(\mathbb R)$ for $1<p\leq 2$.

Gradient of the solution for Poisson equation

For which $p$ is $\frac{1}{x^a+x^b}$ in $\cal{L}^p$?

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