Optimal Gaussian Sobolev embeddings
By Andrea Cianchi, L. Pick. 2009
50 citations recorded by the source corpus.
Abstract A reduction theorem is established, showing that any Sobolev inequality, involving arbitrary rearrangement-invariant norms with respect to the Gauss measure in R n , is equivalent to a one-dimensional inequality, for a suitable Hardy-type operator, involving the same norms with respect to the standard Lebesgue measure on the unit interval. This result is exploited to provide a general characterization of optimal range and domain norms in Gaussian Sobolev inequalities. Applications to special instances yield optimal Gaussian Sobolev inequalities in Orlicz and Lorentz(–Zygmund) spaces, point out new phenomena, such as the existence of self-optimal spaces, and provide further insight into classical results.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3d67a1bf566fd65e3121cc135f8d45afd51fb8a5
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In Applied Mathematics
- Joaquim Martín
- Lenka Slav'ikov'a
- L. Pick
- Mario Milman
- Andrea Cianchi
- Iwona Chlebicka
- Cristina Tarsi
- Robert J. Berman
In Mathematical Physics
- Joaquim Martín
- Mario Milman
- Lenka Slav'ikov'a
- L. Pick
- Andrea Cianchi
- Iwona Chlebicka
- P. Hasto
- Giulio Ciraolo
Citations in the corpus
- Pointwise symmetrization inequalities for Sobolev functions and applications (2009, methodology): “[86], and also [39]), we can use Theorem 11 to transfer to Q the Gaussian Poincaré inequalities.”
- Higher-order Sobolev embeddings and isoperimetric inequalities (2013, background): “A proof for arbitrary rearrangement-invariant norms, in Gauss space, is given in [32].”