Application of Perron Trees to Geometric Maximal Operators

Anthony Gauvan (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LMO - Laboratoire de Mathématiques d'Orsay

To be able to construct a generalized Perron trees as in [11] with a family of triangles T implies that the maximal operator MT associated to this family is unbounded on Lp(R2) for any 1 ≤ p < ∞. If T ′ is a family of triangles which is geometrically adapted to the family T , we prove that MT′ is also unbounded on Lp(R2) for any 1 ≤ p < ∞.

Domaines: Analyse fonctionnelle [math.FA]; Analyse classique [math.CA]

Anthony Gauvan. Application of Perron Trees to Geometric Maximal Operators. 2021. ⟨hal-03295909v1⟩