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On the Summing Property of the Sobolev Embedding Operators

Authors:	Wojciechowski M

Abstract:	We prove that the Sobolev embedding operator S _d,k,p : $L_{(k)}^p (\mathbb{T}^d )$ $L^s (\mathbb{T}^d )$ , where 1/s=1/p-k/d , is (v,1) -absolutely summing for appropriate v > 1 . The result is optimal for s $\leqslant$ 2 .

Keywords:	absolutely summing operators Sobolev spaces
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