Interpolation on Sparse Grids and Nikol'skijbesov Spaces of Dominating Mixed Smoothness Running Title: Interpolation on Sparse Grids and Nikol'skijjbesov Spaces

We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of Nikol'skij Besov spaces of dominating mixed smoothness. The main ingredients are a uni ed approach to error estimates in univariate Nikol'skij Besov spaces and the tensor product characterization of the bivariate Nikol'skij Besov spaces of dominating mixed smoothness.

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