Averages andK-Functionals Related to the Laplacian

@inproceedings{Ditzian1999AveragesAR,
  title={Averages andK-Functionals Related to the Laplacian},
  author={Zeev Ditzian and K. V. Runovskii},
  year={1999}
}
ForRdorTd, averages on balls and spheres are shown to satisfy an equivalence relation withK-functionals that are generated by the Laplacian. The converse result is given in terms of strong converse inequality of type A and type D for the averages on the Ball and on the sphere, respectively. Combinations of averages on concentric balls and spheres yield strong converse results of type B for higher levels of smoothness. 

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