A new proof is given for a theorem by V. G. Maz'ya. It gives a necessary and sufficient condition on the open set Ω in$R$^{$N$}for the functions in$W$_{0}^{$m,p$}(Ω) to have the ordinary norm equivalent to the norm obtained when including only the highest order derivatives in the definition. The proof is based on a kind of polynomial capacities, Maz'ya capacities.

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We prove the almost everywhere convergence of the inverse spherical transform of$L$_{$p$}bi-$K$-invariant functions on the group$SL$(2,$R$), 4/3<$p$≤2. The result appears to be sharp.

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