Abstract
We describe a space of functions contained inxxLx℞(D)⋂C(D ⋃G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLxa2 and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC*-subalgebra ofxxLx℞(D) which we conjecture to be a proper super-set ofU.
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