query: Applying Hölder inequality to prove $\Vert x \Vert_p \leq n^{\frac{1}{p}-\frac{1}{q}} \Vert x \Vert_q$
positive_passages.docid: 20844
positive_passages.text: Relations between p norms
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 26828
negative_passages.text: Generalization of Hölder inequality
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 132431
negative_passages.text: Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
negative_passages.docid: 116685
negative_passages.text: Reciprocal of Holder's inequality
negative_passages.docid: 41293
negative_passages.text: Prove the inequalities $|z_1 +z_2| \geq \frac{1}{2}(|z_1|+|z_2|)|\frac {z_1} {|z_1|} +\frac {z_2} {|z_2|}|$
negative_passages.docid: 34349
negative_passages.text: Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 144500
negative_passages.text: Cauchy-Schwarz inequality proof (but not the usual one)
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities
negative_passages.docid: 63124
negative_passages.text: Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
negative_passages.docid: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 3110
negative_passages.text: Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
negative_passages.docid: 139674
negative_passages.text: Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality