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At the moment, there are a lot of routines which take an "axes" keyword, and in many of these, it could be avoided altogether or reduced to an integer.

Example 1: the "weight" method of DomainObject and derived classes

Here, axes is mostly used to determine, which particular axes in a Field belong to the space. In principle, all of this could be avoided if this method simply returned an array with one weight per pixel (or a scalar if all weights are equal), and leave all the juggling with array indices to Field.weight().

As things are, there are various alternative implementations of the re-shaping task (look for example at the weight methods of PowerSpace and GLSpace).

My suggestion is to simplify DomainObject's weight method to:

def volfactor(self):
    """ Returns an array containing the object's volume factors.
    The array must be broadcastable to the space's dimensions
    (useful if the volume factors are uniform in a direction, e.g. for GLSpace).
    Alternatively, if all volume factors are equal, returns a scalar.
    """

... and leave all the operations involving powers, reshaping etc. to the calling Field.weight method.

Example 2: Space.hermitianize_decomposition():

Here the axes variable always contains a tuple with as many entries as the space has dimensions, and the entries take the form i, i+1, i+2, ... I suggest to pass a scalar integer with the name first_axis instead, which should be less error-prone.

If there is agreement to go into this direction, there are more cases, but we can discuss them later :)