If $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$ then $\|fg\|_{L^r}\leq \|f\|_{L^p}\|g\|_{L^q}$
26828
Generalization of Hölder inequality
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$
72906
Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
24777
If $f$ is measurable and $fg$ is in $L^1$ for all $g \in L^q$, must $f \in L^p$?
108782
Inequality $\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1} \ge 1$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
100608
Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
99676
Prove $\sum{\frac{1}{(x+2y)^2}} \geq\frac{1}{xy+yz+zx}$
64486
Show that for non-negative measurable functions $f,g$ with $fg \geq 1$ the inequality $(\int f^p)(\int g^p) \geq 1$ holds.
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
34349
Prove that $\frac{1}{1+x_1}+\frac{1}{1+x_2}+\cdots+\frac{1}{1+x_n} \geq \frac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$
110093
Proving that the solution to $f^{\prime}(x) = \frac{1}{x^{2} + (f(x))^{2}}$ is bounded above.