The norm $\| \cdot \|_1$ measures the area under the absolute value of the function. But what is the intuition behind measuring the area under the $p$-th power of the absolute value? What kind of information does that give about the function? How can it be interpreted that a function is in $L^p$ but not in $L^q $ for $p \neq q$?
2026-04-05 14:54:41.1775400881
Intuition behind the $\| \cdot \|_p$-norm?
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