Sampling Inequalities and Fractional-Order Sobolev Semi-norms with Operator Theoretical Differences

Abstract

An extension of a bound on functions in Sobolev spaces with Scattered zeroes and applications to radial basis function surface fitting,spline interpolation,smoothing and polynomial are shown.The characterizations of interpolation of Bosevspaces and on domains in Euclidean spaces are discussed, sampling inequalities to Sobolev semi-norms,spaces of fractional order and derivatives data are determined.We use the method of Carlesonmeasures and operator theoretic differences between Hardy and spaces of Dirichlettype.The duality of an inequality, embedding derivatives with related inequalities one given.