New posts in Lp Spaces

If $X\subset L^1$ is a closed vector space and $X\subset \bigcup_{1<p\leq\infty} L^p$ then $X\subset L^q$ for some $q>1$.

derivative of the $L^p$-norm with respect to $p$

Uniform bound for integral in terms of $\left\lVert f' \right\rVert_4^4$

If $T:(\mathbb{R}^2,\|\cdot\|_p) \to (\mathbb{R}^2,\|\cdot\|_q)$ is an onto linear isometry, then must it be $p=q$?

How is the dominated convergence theorem applied here?

Completitude of $L^1[0,1]\cap L^2[0,1]$ with the maximumm norm

Can we approximate a vector field on the plane with non-vanishing vector fields in $L^2$?

Convolution of an $L^p$ function with a Compactly supported continuous function. What does it give?

If $L^1$ average of $f$ is smaller than $t^2$ then $f=0$ a.e.

Minimize $q\mapsto\int\frac{(pf)^2}q\:{\rm d}\lambda$ subject to $\int q\:{\rm }\lambda=1$ using the method of Lagrange multipliers