Maybe I was not so clear.
I said “in the sliding window way” means, convolution operate take a patch of x to do the linear operation.
Looks like:
          
            
           39

Every point of the output feature map is got from a patch of x. Note x_patch here.
Now, the lp norm is also implemented in x_patch.
Or we can say, the original 1d convolution is:

And I want:
 2