query: Show that $L^p(U) \subseteq L^q(U)$ for $p > q \geq1$.
positive_passages.docid: 29655
positive_passages.text: $L^p$ and $L^q$ space inclusion
negative_passages.docid: 95266
negative_passages.text: Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
negative_passages.docid: 38761
negative_passages.text: Is the $ L^{p}$$[0,1]$ norm continuous in p?
negative_passages.docid: 81302
negative_passages.text: Showing that $a_n \in \ell^{\infty}$
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: 83291
negative_passages.text: Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
negative_passages.docid: 142812
negative_passages.text: Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$
negative_passages.docid: 63529
negative_passages.text: How to show that this set is compact in $\ell^2$
negative_passages.docid: 118272
negative_passages.text: Show that $L^1$ is strictly contained in $(L^\infty)^*$
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 83959
negative_passages.text: If $f \in L_p \cap L_q$, $1 \leq p < r < q < \infty$ then $f \in L_r$.
negative_passages.docid: 123005
negative_passages.text: $L^p$ Spaces, Young's Theorem, Convolutions, and Minkowski's Inequality
negative_passages.docid: 154076
negative_passages.text: How to show this property of $\mathbb{RP}^{n}$.
negative_passages.docid: 58347
negative_passages.text: $L^p$ spaces and counting measure
negative_passages.docid: 102079
negative_passages.text: If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
negative_passages.docid: 70926
negative_passages.text: Showing that for $n\geq 3$ the inequality $(n+1)^n<n^{(n+1)}$ holds