Hilbert scales and Sobolev spaces defined by associated Legendre functions. (arXiv:0909.4266v1 [math.CA])

In this paper we study the Hilbert scales defined by the associated Legendre
functions for arbitrary integer values of the parameter. This problem is
equivalent to study the left-definite spectral theory associated to the
modified Legendre equation. We give several characterizations of the spaces as
weighted Sobolev spaces and prove identities among the spaces corresponding to
lower regularity index.

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Original source : http://arxiv.org/abs/0909.4266...