We prove an Adams type inequality for unbounded domains in R^4 and in particular for R^4. We prove that for a suitable norm, the Adams functional is bounded by a constant independent of the domain. Furthermore, we generalize this result to arbitrary Sobolev spaces of even order.
Sharp Adams-type inequalities in R^n / B. Ruf, F. Sani. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 365:2(2012), pp. 645-670. [10.1090/S0002-9947-2012-05561-9]
Sharp Adams-type inequalities in R^n
B. RufPrimo
;F. SaniSecondo
2012
Abstract
We prove an Adams type inequality for unbounded domains in R^4 and in particular for R^4. We prove that for a suitable norm, the Adams functional is bounded by a constant independent of the domain. Furthermore, we generalize this result to arbitrary Sobolev spaces of even order.
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