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Some capacitary strong type inequalities and related function spaces
Keng Hao Ooi, Nguyen Cong Phuc
https://arxiv.org/abs/2510.08982 https://arxiv.org/pdf/…

Some capacitary strong type inequalities and related function spaces
We verify a conjecture of D. R. Adams on a capacitary strong type inequality that generalizes the classical capacitary strong type inequality of V. G. Maz'ya. As a result, we characterize related function spaces as Köthe duals to a class of Sobolev multiplier type spaces. Moreover, using tools from nonlinear potential theory, weighted norm inequalities, and Banach function space theory, we show that these spaces are also isomorphic to more concrete spaces that are easy to use and fit in well w…

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