Approximation by sampling-type operators in $L_p$-spaces

Approximation properties of the sampling-type quasi-projection operators $Q_j(f,φ, \widetildeφ)$ for functions $f$ from anisotropic Besov spaces are studied. Error estimates in $L_p$-norm are obtained for a large class of tempered distributions $\widetildeφ$ and a large class of functions $φ$ under the assumptions that $φ$ has enough decay, satisfies the Strang-Fix conditions and a compatibility condition with $\widetildeφ$. The estimates are given in terms of moduli of smoothness and best approximations.

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