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We prove Adams’ type inequalities with radial increasing mass weights in the whole \(\mathbb R^4\) , in the setting of mass-weighted Sobolev spaces \(H_w^{2}(\mathbb R^4)\) . Due to the presence of increasing weights, the reduction to radial functions via rearrangement arguments is not permitted. The proofs mainly rely on a proper change of variables, which allows us to establish an isomorphism between \(H_w^2(\mathbb R^4)\) and \(H^2(\mathbb R^4)\) .

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Adams’ Type Inequalities in the Whole \(\mathbb R^4\) with Increasing Weights

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  • 发表日期：

    2025年

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  • Cristina Tarsi

摘要

We prove Adams’ type inequalities with radial increasing mass weights in the whole \(\mathbb R^4\) , in the setting of mass-weighted Sobolev spaces \(H_w^{2}(\mathbb R^4)\) . Due to the presence of increasing weights, the reduction to radial functions via rearrangement arguments is not permitted. The proofs mainly rely on a proper change of variables, which allows us to establish an isomorphism between \(H_w^2(\mathbb R^4)\) and \(H^2(\mathbb R^4)\) .