We prove a family of sharp multilinear integral inequalities on real spheres involving functions that possess some symmetries that can be described by annihilation by certain sets of vector fields. The Lebesgue exponents involved are seen to be related to the combinatorics of such sets of vector fields. Moreover, we derive some Euclidean Brascamp–Lieb inequalities localized to a ball of radius R, with a blow-up factor of type R^δ, where the exponent δ is related to the aforementioned Lebesgue exponents, and prove that in some cases δ is optimal.

A family of sharp inequalities on real spheres / Bramati, R.. - In: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. - ISSN 1747-6933. - ELETTRONICO. - (2021). [10.1080/17476933.2021.1921754]

A family of sharp inequalities on real spheres

Bramati R.
2021

Abstract

We prove a family of sharp multilinear integral inequalities on real spheres involving functions that possess some symmetries that can be described by annihilation by certain sets of vector fields. The Lebesgue exponents involved are seen to be related to the combinatorics of such sets of vector fields. Moreover, we derive some Euclidean Brascamp–Lieb inequalities localized to a ball of radius R, with a blow-up factor of type R^δ, where the exponent δ is related to the aforementioned Lebesgue exponents, and prove that in some cases δ is optimal.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2927198