Does the following inequality hold in $L^{2}$ space? $$ \left\lVert \sum_{i=1}^{N}\int_{0}^{t} f_{i}(t)dt\right\rVert^{2}_{L^{2}}\leq C\sum_{i=1}^{N} \left\lVert\int_{0}^{t} f_{i}(t)dt\right\rVert^{2}_{L^{2}}$$ Thanks for any help.
2026-03-30 22:48:14.1774910894
Properties of $L^2$ norm
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