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Interpolation of quasicontinuous functions

Joan Cerdà, Joaquim Martín, Pilar Silvestre (2011)

Banach Center Publications

If C is a capacity on a measurable space, we prove that the restriction of the K-functional K ( t , f ; L p ( C ) , L ( C ) ) to quasicontinuous functions f ∈ QC is equivalent to K ( t , f ; L p ( C ) Q C , L ( C ) Q C ) . We apply this result to identify the interpolation space ( L p , q ( C ) Q C , L p , q ( C ) Q C ) θ , q .

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