query: Holder Inequality when $0 < p < 1$
positive_passages.docid: 142785
positive_passages.text: How can I prove Holder inequality for $0<p<1$?
negative_passages.docid: 110876
negative_passages.text: Prove that $p\mid \binom{p}{k},\ 0< k< p$
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 46746
negative_passages.text: How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
negative_passages.docid: 106767
negative_passages.text: $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
negative_passages.docid: 50830
negative_passages.text: Case of equality in Markov's inequality
negative_passages.docid: 109663
negative_passages.text: Random variables for which Markov, Chebyshev inequalities are tight
negative_passages.docid: 147145
negative_passages.text: Interesting short Inequality
negative_passages.docid: 149536
negative_passages.text: Why is the  $L_p$ norm strictly convex for $1<p<\infty?$
negative_passages.docid: 54703
negative_passages.text: Find the a < 0 for which the inequalities have at least one common solutions
negative_passages.docid: 14251
negative_passages.text: $P[X=x]=0$ when $X$ is continuous variable
negative_passages.docid: 139158
negative_passages.text: Inequality concerning nonnegative numbers (related to Hanner's inequalities)
negative_passages.docid: 102019
negative_passages.text: How to solve inequality $1-\frac{1}{x}\geq 0$ correctly?
negative_passages.docid: 138490
negative_passages.text: An inequality with a weird condition
negative_passages.docid: 46760
negative_passages.text: To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
negative_passages.docid: 80873
negative_passages.text: Kind of converse of Kolmogorov maximal inequality