Singular integrals on regular curves in the Heisenberg group
نویسندگان
چکیده
Let H be the first Heisenberg group, and let k ∈ C ∞ ( ∖ { 0 } ) a kernel which is either odd or horizontally odd, satisfies | ∇ n p ≤ ‖ − 1 , ≥ . The simplest examples include certain Riesz-type kernels considered by Chousionis Mattila, = log We prove that convolution with as above, yields an L 2 -bounded operator on regular curves in This extends theorem of G. David to group. As corollary our main result, we infer all 3-dimensional yield bounded operators Lipschitz flags needed for solving sub-elliptic boundary value problems domains via method layer potentials. details are contained separate paper. Finally, technique new results non-negative kernels, introduced Li. Soit le groupe de Heisenberg, et soit un noyau impair ou horizontalement vérifiant la propriété : Les exemples les plus simples comprennent noyaux type Riesz étudiés d'abord par Nous démontrons que comme ci-dessus, définit opérateur borné sur courbes régulières. Ce résultat généralise théorème au Heisenberg. Comme corollaire notre principal, nous déduisons tous impairs dimension 3 définissent des opérateurs bornés certaines surfaces lipschitziennes, appelons « drapeaux », dans Cela permet résoudre potentiel simple double couche problèmes aux limites sous-elliptiques domaines lipschitziens. détails se trouvent autre article. Finalement, méthode donne nouveaux résultats concernant certains non négatifs, introduits
منابع مشابه
p-ESTIMATES FOR SINGULAR INTEGRALS AND MAXIMAL OPERATORS ASSOCIATED WITH FLAT CURVES ON THE HEISENBERG GROUP
The maximal function along a curve (t, γ (t), tγ (t)) on the Heisenberg group is discussed. The L p-boundedness of this operator is shown under the doubling condition of γ ′ for convex γ in R. This condition also applies to the singular integrals when γ is extended as an even or odd function. The proof is based on angular LittlewoodPaley decompositions in the Heisenberg group.
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2021
ISSN: ['0021-7824', '1776-3371']
DOI: https://doi.org/10.1016/j.matpur.2021.07.004