Question

Fourier transform of $\chi_B$ not in $L^1(\mathbb R^n)$ for the unit ball $B$

score 72 · Answer 1 · 2026-05-04 16:51:21

72

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Fourier transform of $\chi_B$ not in $L^1(\mathbb R^n)$ for the unit ball $B$

Published on 04 May 2026 - 16:51

score 81 · Answer 2 · 2026-04-16 05:08:17

81

Views

Show that $\lVert Tf \rVert_{L^2} \leq \sqrt{ab} \lVert f \rVert_{L^2}$

Published on 16 Apr 2026 - 5:08

score 66 · Answer 3 · 2026-04-11 14:29:47

66

Views

How to use the Riemannian metric to compute an integral?

Published on 11 Apr 2026 - 14:29

score 113 · Answer 4 · 2026-04-10 15:48:02

113

Views

Knowing if a function belong to an Lp space

Published on 10 Apr 2026 - 15:48

score 262 · Answer 5 · 2026-04-22 11:27:48

262

Views

Translation invariant operators in $L^p$ spaces

Published on 22 Apr 2026 - 11:27

score 166 · Answer 6 · 2026-04-15 23:17:33

166

Views

A generalized version of dominated convergence theorem for Banach spaces

Published on 15 Apr 2026 - 23:17

score 93 · Answer 7 · 2026-04-13 23:28:20

93

Views

Is this variant of dominated convergence theorem correct?

Published on 13 Apr 2026 - 23:28

score 63 · Answer 8 · 2026-04-17 02:01:06

63

Views

Is it true that $f_n \to f$ $\mu$-a.e. and $\int f_n \to \int f$ imply $\|f_n\|_1 \to \|f\|_1$?

Published on 17 Apr 2026 - 2:01

score 57 · Answer 9 · 2026-04-12 07:28:51

57

Views

continuous/smooth Fourier transform

Published on 12 Apr 2026 - 7:28

score 43 · Answer 10 · 2026-04-13 02:27:31

43

Views

Is my generalization of Theorem 4.14 in Brezis's Functional Analysis correct?

Published on 13 Apr 2026 - 2:27

score 118 · Answer 11 · 2026-04-15 18:19:28

118

Views

Let $E$ be a uniformly convex Banach space and $p \in (1, \infty)$. Is $L_p(X, \mu, E)$ uniformly convex?

Published on 15 Apr 2026 - 18:19

score 61 · Answer 12 · 2026-04-11 15:00:05

61

Views

Reference request: If $E$ is a reflexive Banach space, then $L_p(X, \mu, E)$ is reflexive and $(L_p(X, \mu, E))^* = L_q(X, \mu, E^*)$

Published on 11 Apr 2026 - 15:00

score 60 · Answer 13 · 2026-04-16 14:19:38

60

Views

$f\in L^1\cap L^2$ with $\|f\|_1=a, \|f\|_2=b$

Published on 16 Apr 2026 - 14:19

score 147 · Answer 14 · 2026-04-14 01:31:47

147

Views

Can we approximate a real-analytic function and its derivatives by non-analytic smooth functions in the following way?

Published on 14 Apr 2026 - 1:31

score 71 · Answer 15 · 2026-04-16 17:00:29

71

Views

$\lim\limits_{n\to\infty}\int_\mathbb R |f_n-f|d\lambda=0 \leftrightarrow \lim \inf_{n\in\mathbb N}f_n\leq f$

Published on 16 Apr 2026 - 17:00

List Question

Fourier transform of $\chi_B$ not in $L^1(\mathbb R^n)$ for the unit ball $B$

Show that $\lVert Tf \rVert_{L^2} \leq \sqrt{ab} \lVert f \rVert_{L^2}$

How to use the Riemannian metric to compute an integral?

Knowing if a function belong to an Lp space

Translation invariant operators in $L^p$ spaces

A generalized version of dominated convergence theorem for Banach spaces

Is this variant of dominated convergence theorem correct?

Is it true that $f_n \to f$ $\mu$-a.e. and $\int f_n \to \int f$ imply $\|f_n\|_1 \to \|f\|_1$?

continuous/smooth Fourier transform

Is my generalization of Theorem 4.14 in Brezis's Functional Analysis correct?

Let $E$ be a uniformly convex Banach space and $p \in (1, \infty)$. Is $L_p(X, \mu, E)$ uniformly convex?

Reference request: If $E$ is a reflexive Banach space, then $L_p(X, \mu, E)$ is reflexive and $(L_p(X, \mu, E))^* = L_q(X, \mu, E^*)$

$f\in L^1\cap L^2$ with $\|f\|_1=a, \|f\|_2=b$

Can we approximate a real-analytic function and its derivatives by non-analytic smooth functions in the following way?

$\lim\limits_{n\to\infty}\int_\mathbb R |f_n-f|d\lambda=0 \leftrightarrow \lim \inf_{n\in\mathbb N}f_n\leq f$

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