diff --git a/nifty4/operators/fft_smoothing_operator.py b/nifty4/operators/fft_smoothing_operator.py
index d3c3ee8a9b93e5e5e1b3198a5e7333fdc7eb80b5..239b6e1dae41e05c70d535e4704879e495718a01 100644
--- a/nifty4/operators/fft_smoothing_operator.py
+++ b/nifty4/operators/fft_smoothing_operator.py
@@ -24,6 +24,30 @@ from ..domain_tuple import DomainTuple
 
 
 def FFTSmoothingOperator(domain, sigma, space=None):
+    """ This function returns an operator that carries out a smoothing with
+    a Gaussian kernel of width `sigma` on the part of `domain` given by
+    `space`.
+
+    Parameters
+    ----------
+    domain : Domain, tuple of Domains, or DomainTuple
+       The total domain of the operator's input and output fields
+
+    sigma : float>=0
+       The sigma of the Gaussian used for smoothing. It has the same units as
+       the RGSpace the operator is working on.
+       If `sigma==0`, an identity operator will be returned.
+
+    space: integer, *optional*
+       The index of the sub-domain on which the smoothing is performed.
+       Can be omitted if `domain` only has one sub-domain.
+
+    Notes
+    -----
+       The sub-domain on which the smoothing is carried out *must* be a
+       non-harmonic `RGSpace`.
+    """
+
     sigma = float(sigma)
     if sigma < 0.:
         raise ValueError("sigma must be nonnegative")