2020/07/02 by Gonzalo H. Ibañez-Firnkorn, Ibañez-Firnkorn, Gonzalo H., María Silvina Riveros +3
Mathematics · #Advanced Harmonic Analysis Research #Applied mathematics #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical economics #Mathematics #math.CA
paper · pdf · doi:10.48550/arxiv.2007.01400
arxiv created 2020/07/02 · openalex publication_date 2020/07/02 · arxiv updated 2020/07/06 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28
Let 0≤ α<n, m∈ ℕ and let consider Tα,m be a of integral operator, given by kernel of the form K(x,y)=k1(x-A1y)k2(x-A2y)… km(x-Amy), where Ai are invertible matrices and each ki satisfies a fractional size and generalized fractional Hörmander condition. In [Ibañez-Firnkorn, G. H., and Riveros, M. S. (2018). Certain fractional type operators with Hörmander conditions. To appear in Ann. Acad. Sci. Fenn. Math.] it was proved that Tα,m is controlled in Lp(w)-norms, w∈ A∞, by the sum of maximal operators MAi-1,α. In this paper we present the class of weights AA,p,q, where A is an invertible matrix. This class are the good weights for the weak-type estimate of MA-1,α. For certain kernels ki we can characterize the weights for the strong-type estimate of Tα,m. Also, we give a the strong-type estimate using testing conditions.