Question

Embedding of differentiable functions into Holder Functions

score 71 · Answer 1 · 2023-07-04 11:11:44

71

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Embedding of differentiable functions into Holder Functions

Published on 04 Jul 2023 - 11:11

score 207 · Answer 2 · 2026-02-23 19:13:47

207

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A Holder-continuous function differentiable a.e. is absolutely continuous?

Published on 23 Feb 2026 - 19:13

score 89 · Answer 3 · 2023-07-27 15:39:24

89

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For a Holder-continuous function, is the quotient $\frac{\lvert f(x)-f(y) \rvert}{\lvert x-y\rvert^{\alpha}}$ jointly continuous for $x \neq y$?

Published on 27 Jul 2023 - 15:39

score 34 · Answer 4 · 2023-08-23 13:47:12

34

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definition of BUC($\alpha,\frac{\alpha}{2})$

Published on 23 Aug 2023 - 13:47

score 49 · Answer 5 · 2023-09-16 12:17:48

49

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A property of $C^{0, \alpha}$ functions

Published on 16 Sep 2023 - 12:17

score 98 · Answer 6 · 2023-10-05 23:26:28

98

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What is the relationship between Hölder spaces and differentiability?

Published on 05 Oct 2023 - 23:26

score 54 · Answer 7 · 2023-10-06 02:47:34

54

Views

Holder continuity in an interval implies boundedness

Published on 06 Oct 2023 - 2:47

score 52 · Answer 8 · 2023-10-07 15:32:33

52

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Reverse Holder functions

Published on 07 Oct 2023 - 15:32

score 40 · Answer 9 · 2023-10-11 16:05:50

40

Views

Regularity of functions approximated by polynomials

Published on 11 Oct 2023 - 16:05

score 28 · Answer 10 · 2023-10-14 18:15:48

28

Views

If $f$ is Holder of order $\alpha$, then $f'$ is holder of order $\alpha-1$

Published on 14 Oct 2023 - 18:15

score 98 · Answer 11 · 2024-01-10 08:52:12

98

Views

Is there a constant $c>0$ such that $\|(1-\Delta)^{\frac{\alpha}{2}} f\|_\infty\le c\|f\|_{C^{0,\alpha}}$ for all $f \in C^{0,\alpha} (\mathbb{R}^d)$?

Published on 10 Jan 2024 - 8:52

score 48 · Answer 12 · 2026-03-25 09:29:59

48

Views

Is there a constant $c>0$ such that $\| (1-\Delta)^{-\alpha} P^\kappa_t f\|_{C^{n,\beta}_b}\le c t^{-(\frac{n}{2} - \alpha)^+} \| f \|_{C^{\beta}_b}$?

Published on 25 Mar 2026 - 9:29

score 72 · Answer 13 · 2026-02-23 08:39:57

72

Views

Canonical lift of a smooth path as a rough path

Published on 23 Feb 2026 - 8:39

score 22 · Answer 14 · 2024-01-11 20:18:51

22

Views

Interpolation Inequalities in Lebesgue Spaces and Compactness in Hölder Spaces: Proving Norm Relations and Compact Embeddings

Published on 11 Jan 2024 - 20:18

score 24 · Answer 15 · 2024-01-11 20:22:36

24

Views

Proving the Compact Embedding of $C^{0, \alpha}(K)$ into $C^{0, \beta}(K)$

Published on 11 Jan 2024 - 20:22

List Question

Embedding of differentiable functions into Holder Functions

A Holder-continuous function differentiable a.e. is absolutely continuous?

For a Holder-continuous function, is the quotient $\frac{\lvert f(x)-f(y) \rvert}{\lvert x-y\rvert^{\alpha}}$ jointly continuous for $x \neq y$?

definition of BUC($\alpha,\frac{\alpha}{2})$

A property of $C^{0, \alpha}$ functions

What is the relationship between Hölder spaces and differentiability?

Holder continuity in an interval implies boundedness

Reverse Holder functions

Regularity of functions approximated by polynomials

If $f$ is Holder of order $\alpha$, then $f'$ is holder of order $\alpha-1$

Is there a constant $c>0$ such that $\|(1-\Delta)^{\frac{\alpha}{2}} f\|_\infty\le c\|f\|_{C^{0,\alpha}}$ for all $f \in C^{0,\alpha} (\mathbb{R}^d)$?

Is there a constant $c>0$ such that $\| (1-\Delta)^{-\alpha} P^\kappa_t f\|_{C^{n,\beta}_b}\le c t^{-(\frac{n}{2} - \alpha)^+} \| f \|_{C^{\beta}_b}$?

Canonical lift of a smooth path as a rough path

Interpolation Inequalities in Lebesgue Spaces and Compactness in Hölder Spaces: Proving Norm Relations and Compact Embeddings

Proving the Compact Embedding of $C^{0, \alpha}(K)$ into $C^{0, \beta}(K)$

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