Question

Prove the space $L^p(X) \cap L^q(X)$ with the norm $||f||_{L^p \cap L^q}=||f||_p+||f||_q$ is a Banach space

score 282 · Answer 1 · 2026-03-28 14:56:49

282

Views

Prove the space $L^p(X) \cap L^q(X)$ with the norm $||f||_{L^p \cap L^q}=||f||_p+||f||_q$ is a Banach space

Published on 28 Mar 2026 - 14:56

score 38 · Answer 2 · 2020-03-24 13:14:58

38

Views

Every function in $L^1$ can be expressed as a product of functions in $L^p$ and $L^{P^*}$

Published on 24 Mar 2020 - 13:14

score 1.2k · Answer 3 · 2026-03-30 03:34:48

1.2k

Views

Approximate $L^2$ function by convolving with mollifiers

Published on 30 Mar 2026 - 3:34

score 870 · Answer 4 · 2026-04-04 20:25:41

870

Views

Convergence of Approximations of the Identity in $L^p(\mathbb R^d)$

Published on 04 Apr 2026 - 20:25

score 83 · Answer 5 · 2020-03-25 21:04:06

83

Views

Double Sequence Defines a Bounded Linear Map on l2

Published on 25 Mar 2020 - 21:04

score 2.1k · Answer 6 · 2020-03-26 06:51:19

2.1k

Views

Geometric definition of the dot product in $n$-dimensional vector spaces

Published on 26 Mar 2020 - 6:51

score 108 · Answer 7 · 2026-03-28 11:34:16

108

Views

Inverse Fourier Tranform of $e^{-|\xi|^{2s}}$ is in $L^p$

Published on 28 Mar 2026 - 11:34

score 325 · Answer 8 · 2020-03-26 10:51:23

325

Views

Is there a deep reason why strong estimates fail to exist for $L^1$ so often?

Published on 26 Mar 2020 - 10:51

score 90 · Answer 9 · 2026-03-25 23:42:17

90

Views

If $u_n \in L^\infty(0,T;L^\infty)$ and $u_n \rightharpoonup^* u$ in $L^\infty((0,T)\times \Omega)$, is $u \in L^\infty(0,T;L^\infty)$?

Published on 25 Mar 2026 - 23:42

score 18 · Answer 10 · 2026-03-21 22:20:02

18

Views

How to compare integral for decreasing function on some ball?

Published on 21 Mar 2026 - 22:20

score 23 · Answer 11 · 2020-03-27 10:54:08

23

Views

$\int_{\{ |x|\leq 5C \}} (1+|x|^2)^{ps} dx \leq C_1(C) \int_{\{ |x|\leq 5 \}} (1+|x|^2)^{ps} dx$?

Published on 27 Mar 2020 - 10:54

score 140 · Answer 12 · 2026-03-26 04:20:02

140

Views

Let $S$ denote Schwartz space , $T:L^p \to L^p$ be a linear operator . If the restriction of $T$ on $S$ is bounded , can we show that $T$ is bounded?

Published on 26 Mar 2026 - 4:20

score 13 · Answer 13 · 2026-03-01 07:01:56

13

Views

Let $g_n =e^{x} f_n \in L_1$ and $g=e^{x} f \in L_1$ with $f_n, f\in L_1$. If $f_n \to f$ in $L_1$ does $g_n \to g$ in $L_1$

Published on 01 Mar 2026 - 7:01

score 35 · Answer 14 · 2026-02-23 06:58:24

35

Views

Compact closure in $C(\overline{\omega})$ implies compact closure in $L^p(\omega)$?

Published on 23 Feb 2026 - 6:58

score 136 · Answer 15 · 2026-04-05 18:39:26

136

Views

Convergence in measure implies $L^1$-convergence assuming $||f_n||_{L^p}$ is unif. bounded

Published on 05 Apr 2026 - 18:39

List Question

Prove the space $L^p(X) \cap L^q(X)$ with the norm $||f||_{L^p \cap L^q}=||f||_p+||f||_q$ is a Banach space

Every function in $L^1$ can be expressed as a product of functions in $L^p$ and $L^{P^*}$

Approximate $L^2$ function by convolving with mollifiers

Convergence of Approximations of the Identity in $L^p(\mathbb R^d)$

Double Sequence Defines a Bounded Linear Map on l2

Geometric definition of the dot product in $n$-dimensional vector spaces

Inverse Fourier Tranform of $e^{-|\xi|^{2s}}$ is in $L^p$

Is there a deep reason why strong estimates fail to exist for $L^1$ so often?

If $u_n \in L^\infty(0,T;L^\infty)$ and $u_n \rightharpoonup^* u$ in $L^\infty((0,T)\times \Omega)$, is $u \in L^\infty(0,T;L^\infty)$?

How to compare integral for decreasing function on some ball?

$\int_{\{ |x|\leq 5C \}} (1+|x|^2)^{ps} dx \leq C_1(C) \int_{\{ |x|\leq 5 \}} (1+|x|^2)^{ps} dx$?

Let $S$ denote Schwartz space , $T:L^p \to L^p$ be a linear operator . If the restriction of $T$ on $S$ is bounded , can we show that $T$ is bounded?

Let $g_n =e^{x} f_n \in L_1$ and $g=e^{x} f \in L_1$ with $f_n, f\in L_1$. If $f_n \to f$ in $L_1$ does $g_n \to g$ in $L_1$

Compact closure in $C(\overline{\omega})$ implies compact closure in $L^p(\omega)$?

Convergence in measure implies $L^1$-convergence assuming $||f_n||_{L^p}$ is unif. bounded

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