Question

Convolution of L^p and L^q function is uniformly continuous or not?

score 2.9k · Answer 1 · 2026-04-14 02:50:36

2.9k

Views

Convolution of L^p and L^q function is uniformly continuous or not?

Published on 14 Apr 2026 - 2:50

score 82 · Answer 2 · 2026-04-17 06:27:11

82

Views

Show that $\lim_{a\rightarrow0+}a^{p}\omega(a)=\lim_{b\rightarrow\infty}b^{p}\omega(b)=0$

Published on 17 Apr 2026 - 6:27

score 450 · Answer 3 · 2026-04-21 16:09:50

450

Views

Fourier inversion for $f \in L^p(\mathbb R^n)$ and $\hat f \in L^1(\mathbb R^n)$ , where $1<p<2$

Published on 21 Apr 2026 - 16:09

score 297 · Answer 4 · 2026-04-21 16:12:57

297

Views

Well-defined ness of defining Fourier transform of functions in $L^p$ ,for $1<p<2$, by decomposing as a sum of $L^1$ and$L^2$ functions

Published on 21 Apr 2026 - 16:12

score 40 · Answer 5 · 2026-04-21 16:09:32

40

Views

Equivalence of sequence approximation and sum decomposition definition of Fourier transform

Published on 21 Apr 2026 - 16:09

score 706 · Answer 6 · 2026-04-14 09:21:54

706

Views

There is a function in weak $L^1$ but not in $L^1$

Published on 14 Apr 2026 - 9:21

score 1.5k · Answer 7 · 2026-04-06 07:20:57

1.5k

Views

Normability of weak $L^p$-spaces

Published on 06 Apr 2026 - 7:20

score 70 · Answer 8 · 2026-04-17 00:34:49

70

Views

Proving that $\|f\|_\infty=\sup\{M:\mu(\{x:|f(x)|>M\})>0\}$

Published on 17 Apr 2026 - 0:34

score 48 · Answer 9 · 2026-04-16 20:54:52

48

Views

Proving that $\displaystyle\int_0^\infty f(t)\frac{\sin(xt)}{t}dt$ exist for $f\in\mathcal{L}^p(0,\infty)$, $1<p<\infty$ and $x>0$

Published on 16 Apr 2026 - 20:54

score 110 · Answer 10 · 2026-04-15 11:50:04

110

Views

Under what conditions does $f$ belong to $L^{p}(\mathbb{R}^{N} )$?

Published on 15 Apr 2026 - 11:50

score 252 · Answer 11 · 2026-04-17 15:36:19

252

Views

If f+g in L2 then so are f and g

Published on 17 Apr 2026 - 15:36

score 118 · Answer 12 · 2026-04-12 20:15:57

118

Views

Question for the proof of $L^p$ space

Published on 12 Apr 2026 - 20:15

score 167 · Answer 13 · 2026-04-12 01:39:40

167

Views

A function with Fourier coefficients in $\ell^1$ is continuous

Published on 12 Apr 2026 - 1:39

score 62 · Answer 14 · 2026-04-12 20:19:54

62

Views

$L^2$ but not $L^{\infty}$

Published on 12 Apr 2026 - 20:19

score 799 · Answer 15 · 2026-04-14 05:53:10

799

Views

Density in the uniform norm and in $L^p$ norm

Published on 14 Apr 2026 - 5:53

List Question

Convolution of L^p and L^q function is uniformly continuous or not?

Show that $\lim_{a\rightarrow0+}a^{p}\omega(a)=\lim_{b\rightarrow\infty}b^{p}\omega(b)=0$

Fourier inversion for $f \in L^p(\mathbb R^n)$ and $\hat f \in L^1(\mathbb R^n)$ , where $1<p<2$

Well-defined ness of defining Fourier transform of functions in $L^p$ ,for $1<p<2$, by decomposing as a sum of $L^1$ and$L^2$ functions

Equivalence of sequence approximation and sum decomposition definition of Fourier transform

There is a function in weak $L^1$ but not in $L^1$

Normability of weak $L^p$-spaces

Proving that $\|f\|_\infty=\sup\{M:\mu(\{x:|f(x)|>M\})>0\}$

Proving that $\displaystyle\int_0^\infty f(t)\frac{\sin(xt)}{t}dt$ exist for $f\in\mathcal{L}^p(0,\infty)$, $1<p<\infty$ and $x>0$

Under what conditions does $f$ belong to $L^{p}(\mathbb{R}^{N} )$?

If f+g in L2 then so are f and g

Question for the proof of $L^p$ space

A function with Fourier coefficients in $\ell^1$ is continuous

$L^2$ but not $L^{\infty}$

Density in the uniform norm and in $L^p$ norm

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