query: Why is the Holder space with exponent $\alpha>1$ a constant set?
positive_passages.docid: 17343
positive_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
negative_passages.docid: 51267
negative_passages.text: Showing a generalized version of the Hölder inequality for $L^{p}$ spaces
negative_passages.docid: 33114
negative_passages.text: Uniqueness of a continuous extension of a function into a Hausdorff space
negative_passages.docid: 36166
negative_passages.text: Uniform continuity on (0,1) implies boundedness
negative_passages.docid: 135941
negative_passages.text: Derivative of $|x|^\alpha$
negative_passages.docid: 111907
negative_passages.text: Prove that Cantor function is Hölder continuous
negative_passages.docid: 115794
negative_passages.text: When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
negative_passages.docid: 107842
negative_passages.text: Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
negative_passages.docid: 104413
negative_passages.text: Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
negative_passages.docid: 101904
negative_passages.text: Why does this limit exist $x^{x}$
negative_passages.docid: 76234
negative_passages.text: Is this vector-valued map Hölder-continuous?
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 118353
negative_passages.text: For set of positive measure $E$, $\alpha \in (0, 1)$, there is interval $I$ such that $m(E \cap I) > \alpha \, m(I)$
negative_passages.docid: 14516
negative_passages.text: The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
negative_passages.docid: 46892
negative_passages.text: Inclusion of $L^p$ spaces