Abstract

Let = ( ( )) be the abstract space of Bessel potentials and a positive smooth Radon measure on . For 2 , we give necessary and sufficient criteria for the boundedness of from ( ) into ( ), provided is contractive. Among others, we shall prove that the boundedness is equivalent to a capacitary type inequality. Further we give necessary and sufficient conditions for to be compactly embedded in ( ). Our method relies essentially on establishing a capacitary strong type inequality.

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