Question

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

score 143 · Answer 1 · 2026-04-09 21:51:12

143

Views

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

Published on 09 Apr 2026 - 21:51

score 26 · Answer 2 · 2026-04-15 21:21:17

26

Views

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

Published on 15 Apr 2026 - 21:21

score 1.1k · Answer 3 · 2026-05-05 00:09:55

1.1k

Views

Equivalence of norms for the space of Hölder continuous functions

Published on 05 May 2026 - 0:09

score 167 · Answer 4 · 2026-04-14 07:24:39

167

Views

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

Published on 14 Apr 2026 - 7:24

score 44 · Answer 5 · 2026-04-15 19:47:59

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 492 · Answer 6 · 2026-05-10 14:29:00

492

Views

Equivalence between Hölder norms

Published on 10 May 2026 - 14:29

score 387 · Answer 7 · 2026-04-10 21:22:57

387

Views

How to prove that Holder space is normed linear space

Published on 10 Apr 2026 - 21:22

score 171 · Answer 8 · 2026-04-15 10:30:41

171

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 15 Apr 2026 - 10:30

score 375 · Answer 9 · 2026-04-16 02:15:56

375

Views

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

Published on 16 Apr 2026 - 2:15

score 119 · Answer 10 · 2026-04-11 03:59:19

119

Views

A question about Hölder space and Sobolev

Published on 11 Apr 2026 - 3:59

score 45 · Answer 11 · 2026-04-14 20:22:10

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 126 · Answer 12 · 2026-04-28 08:53:37

126

Views

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

Published on 28 Apr 2026 - 8:53

score 74 · Answer 13 · 2026-04-16 08:58:01

74

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 16 Apr 2026 - 8:58

score 55 · Answer 14 · 2026-04-11 02:53:51

55

Views

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

Published on 11 Apr 2026 - 2:53

score 204 · Answer 15 · 2026-04-09 10:37:55

204

Views

Compact Embedding Between Parabolic Holder Spaces

Published on 09 Apr 2026 - 10:37

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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