Sobolev type spaces associated with jacobi differential operators

Sobolev type spaces , associated with the Jacobi differential operators are studied. Some properties including completeness and inclusion are proved. Next, the Jacobi potential is defined as a pseudodifferential operator associated with a precise symbol. The operator is extended to a space of distributions. The L p -space of all such Jacobi potential is defined. It is proved that this space is a Banach space, for under some conditions on s t and α. Also, it is shown that solutions of certain equations involving the Jacobi differential operator belong to these spaces.