Relation between $\mathcal{L}_{1}$ and $\mathcal{L}_{2}$ Norms of a Lebesgue function

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Can $\mathcal{L}_{1}$ norm of a function $f(t)$ be related with its $\mathcal{L}_{2}$ norm as $||f||_{1} \leq ||f||_{\infty} ||f||_{2}$ or something like this?