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On the weighted inequality between the Gagliardo and Sobolev seminorms

Published 27 Feb 2023 in math.CA and math.AP | (2302.14029v1)

Abstract: We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With $A_1$ weights we improve earlier results of Bourgain, Brezis, and Mironescu.

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