2025/07/12 by Agnieszka Hejna, Alexander Nagel, Hejna, Agnieszka +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2507.09399
openalex publication_date 2025/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multi-norm singular integrals and Fourier multipliers were introduced in [29], and one application of these notions was a precise description of the composition of convolution operators with Calderón-Zygmund kernels adapted to n different families of dilations. The description of the resulting operators was given in terms of differential inequalities specified by a matrix \mathbf E, and in terms of dyadic decompositions of the kernels and multipliers. In this paper we extend the analysis of multi-norm structures on ℝd by studying the induced Littlewood-Paley decomposition of the frequency space and various associated square functions. After establishing their L1-equivalence, we use these square functions to define a local multi-norm Hardy space h1E(ℝd). We give several equivalent descriptions of this space, including an atomic characterization. There has been recent work, limited to the 2-dilation case, by other authors. The general n-dilation case treated here is considerably harder and requires new ideas and a more systematic approach.