We investigate a class of nonlocal gradients featuring distinct homogeneities at zero and infinity. We establish a representation formula for such doubly homogeneous operators and derive associated Sobolevtype inequalities. We also propose open questions linked to our results, suggesting directions for future research inspired by the work of Haïm Brezis.
Recovering functions via doubly homogeneous nonlocal gradients / Buccheri, S.; Ponce, A. C.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 363:G12(2025), pp. 1377-1406. [10.5802/crmath.800]
Recovering functions via doubly homogeneous nonlocal gradients
Buccheri S.;Ponce A. C.
2025
Abstract
We investigate a class of nonlocal gradients featuring distinct homogeneities at zero and infinity. We establish a representation formula for such doubly homogeneous operators and derive associated Sobolevtype inequalities. We also propose open questions linked to our results, suggesting directions for future research inspired by the work of Haïm Brezis.File in questo prodotto:
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