New posts in Lp Spaces

Proof of Hardy inequality in $\mathbb{R}^n$

Is L2 norm always smaller than L1 norm even in infinite dimensional space?

Prove that $f \in L^2(\mathbb{R})$ and $||f||_2 \leq 1$.

Question for the proof of $L^p$ space

$||f||_p\to ||f||_\infty$ under general assumptions

Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

$L^{\infty}$ is a Banach Space

If $(f_n)\to0$ in $L^2$ and the derivatives converge in $L^2$, must the limit be 0?

Prove the dual space of $l^p$ is isomorphic to $l^q$ if $\frac{1}{q}+\frac{1}{p}=1$

What is the dual space if the measure is not $\sigma-$finite?