Question

Show that a function of two arguments, which is uniformly Hölder continuous on compact subsets, is jointly continuous

score 140 · Answer 1 · 2018-07-08 13:23:55

140

Views

Show that a function of two arguments, which is uniformly Hölder continuous on compact subsets, is jointly continuous

Published on 08 Jul 2018 - 13:23

score 24 · Answer 2 · 2018-07-20 14:25:28

24

Views

Functions $u \in C^{0,1/2}(\mathbb{R}^n)$ satisfy $\|u\|_{C^0(\mathbb{R}^n)} < \infty$

Published on 20 Jul 2018 - 14:25

score 1.1k · Answer 3 · 2026-03-16 22:59:30

1.1k

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Equivalence of norms for the space of Hölder continuous functions

Published on 16 Mar 2026 - 22:59

score 164 · Answer 4 · 2018-07-25 08:37:25

164

Views

Showing $\|uv\|_{C^\alpha} \leq C(v) \|u\|_{C^\alpha}$ for Hölder functions

Published on 25 Jul 2018 - 8:37

score 41 · Answer 5 · 2018-07-28 14:04:16

If $K⊆ℝ^d$ is compact and $f:[0,T]×K×K→ℝ$ is continuous with $f(t,\;⋅\;,\;⋅\;)∈C^{0+β}$, is $t↦\left\|f(t,\;⋅\;,\;⋅\;)\right\|_{C^{0+β}}$ continuous?

score 486 · Answer 6 · 2018-07-28 17:07:04

486

Views

Equivalence between Hölder norms

Published on 28 Jul 2018 - 17:07

score 384 · Answer 7 · 2018-08-10 01:59:28

384

Views

How to prove that Holder space is normed linear space

Published on 10 Aug 2018 - 1:59

score 167 · Answer 8 · 2018-08-16 01:18:07

167

Views

Let $f\colon\Bbb{R}^2\to \Bbb{R}$ such that $|f(x)-f(y)|\leq \Vert x-y\Vert^2.$ Prove that $f$ is a constant

Published on 16 Aug 2018 - 1:18

score 372 · Answer 9 · 2018-08-29 17:37:44

372

Views

Notions of $\beta$-Hölder smoothness when $\beta\in (1,2]$: are they equivalent?

Published on 29 Aug 2018 - 17:37

score 116 · Answer 10 · 2018-09-01 09:09:25

116

Views

A question about Hölder space and Sobolev

Published on 01 Sep 2018 - 9:09

score 43 · Answer 11 · 2018-09-08 14:17:43

For which $ l \in\mathbb{N} $ and $ \alpha\in[0,1] $ does u belong to the hoelder space $ C^{l,\alpha}(\overline {B_1(0)}) $?

score 122 · Answer 12 · 2026-03-22 11:40:37

122

Views

Singular function that is Holder for all $\alpha<1$

Published on 22 Mar 2026 - 11:40

score 71 · Answer 13 · 2018-10-26 09:12:35

71

Views

Why is $\|\operatorname{Co}(D_{\alpha}X)\|_{\gamma} \|\det [D_{\alpha}X(\alpha)]^{-1}\Vert_{\gamma}\le c\| D_{\alpha}X\|_{\gamma}^{2n-1}$?

Published on 26 Oct 2018 - 9:12

score 52 · Answer 14 · 2018-10-30 01:23:40

52

Views

Is this function which shows infinite concussion near $0$ Hölder continuous?

Published on 30 Oct 2018 - 1:23

score 201 · Answer 15 · 2018-11-06 11:24:47

201

Views

Compact Embedding Between Parabolic Holder Spaces

Published on 06 Nov 2018 - 11:24

List Question

Show that a function of two arguments, which is uniformly Hölder continuous on compact subsets, is jointly continuous

Functions $u \in C^{0,1/2}(\mathbb{R}^n)$ satisfy $\|u\|_{C^0(\mathbb{R}^n)} < \infty$

Equivalence of norms for the space of Hölder continuous functions

Showing $\|uv\|_{C^\alpha} \leq C(v) \|u\|_{C^\alpha}$ for Hölder functions

If $K⊆ℝ^d$ is compact and $f:[0,T]×K×K→ℝ$ is continuous with $f(t,\;⋅\;,\;⋅\;)∈C^{0+β}$, is $t↦\left\|f(t,\;⋅\;,\;⋅\;)\right\|_{C^{0+β}}$ continuous?

Equivalence between Hölder norms

How to prove that Holder space is normed linear space

Let $f\colon\Bbb{R}^2\to \Bbb{R}$ such that $|f(x)-f(y)|\leq \Vert x-y\Vert^2.$ Prove that $f$ is a constant

Notions of $\beta$-Hölder smoothness when $\beta\in (1,2]$: are they equivalent?

A question about Hölder space and Sobolev

For which $ l \in\mathbb{N} $ and $ \alpha\in[0,1] $ does u belong to the hoelder space $ C^{l,\alpha}(\overline {B_1(0)}) $?

Singular function that is Holder for all $\alpha<1$

Why is $\|\operatorname{Co}(D_{\alpha}X)\|_{\gamma} \|\det [D_{\alpha}X(\alpha)]^{-1}\Vert_{\gamma}\le c\| D_{\alpha}X\|_{\gamma}^{2n-1}$?

Is this function which shows infinite concussion near $0$ Hölder continuous?

Compact Embedding Between Parabolic Holder Spaces

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