What is the relationship between convergence uniformly, pointwisely, weakly, in $L^{\infty}$ norm and in $L^{p} $ norm?

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What is the relationship between convergence uniformly, pointwise, weakly, in $L^{\infty}$ norm and in $L^{p}$ norm?

I am quite puzzled by so many convergences, can anybody tell me what is the relationship between them? Thanks in advance!

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