I think we have 3 options
a = nn.Conv1d(3, 3, 3) # in channels 3, out channels 3, kernel size 3
x = torch.randn(1, 3, 6) # batch size 1, 3 channels, 6 length of sequence
a(x).shape

torch.Size([1, 3, 4])
first option
b = nn.LayerNorm([4])

second
b = nn.LayerNorm([3, 4])

third
b = nn.LayerNorm([1, 3, 4])

and then
b(a(x))

in the first case, mean, variance would be like
a.mean([2]), a.var([2], unbiased=False)

second case
a.mean([1, 2]), a.var([1, 2], unbiased=False)

third case
a.mean([0, 1, 2]), a.var([0, 1, 2], unbiased=False)

that is
a.mean(), a.var(unbiased=False)