Example where $f\in L^{2}(\mathbb{R})$, but for all $p\in[1,2)\cup(2,\infty]$ $f\notin L^{p}(\mathbb{R})$.
37736
How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
102585
Why is $L^{\infty}$ not separable?
41173
If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
120623
Unit sphere in $\mathbb{R}^\infty$ is contractible?
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
83959
If $f \in L_p \cap L_q$, $1 \leq p < r < q < \infty$ then $f \in L_r$.
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
99675
A closed ball in $l^{\infty}$ is not compact
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
38911
Squares in $\mathbb{Z}_p$ that are not squares in $\mathbb{Z}$
115004
If $x\notin\mathbb Q$, then $\left|x-\frac{p}{q}\right|<\frac{1}{q^2}$ for infinitely many $\frac{p}{q}$?
59837
Suppose $\mu(X)<\infty$. Show that if $\ f\in\ L^q(X,\mu)$ for some $1\le q<\infty$ then $\ f\in\ L^r(X,\mu)$ for $1\le r<q$
29114
If $f \in L^{p_1}(E) $ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$
42774
Examples of involutions on $\mathbb{R}$
29655
$L^p$ and $L^q$ space inclusion
95074
Separability of $l^{p}$ spaces