2022/08/12 by Yiqun Chen, Chen, Yiqun, Hongchao Jia +3
Mathematics · #42B30 #42B35 #46E35 #47A30 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary 42B20 #Secondary 42B25
paper · pdf · doi:10.48550/arxiv.2208.06266
openalex publication_date 2022/08/12 · openalex created_date 2022/08/16 · openalex updated_date 2026/07/28
Let X be a ball quasi-Banach function space on \mathbb Rn satisfying some mild assumptions. In this article, the authors first find a reasonable version \widetildeT of the Calderón--Zygmund operator T on the ball Campanato-type function space LX,q,s,d(ℝn) with q∈[1,∞), s∈ℤ+n, and d∈(0,∞). Then the authors prove that \widetildeT is bounded on LX,q,s,d(ℝn) if and only if, for any γ∈ℤn+ with |γ|≤ s, T^*(xγ)=0, which is hence sharp. Moreover, \widetildeT is proved to be the adjoint operator of T, which further strengthens the rationality of the definition of \widetildeT. All these results have a wide range of applications. In particular, even when they are applied, respectively, to weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces, Orlicz-slice spaces, Morrey spaces, mixed-norm Lebesgue spaces, local generalized Herz spaces, and mixed-norm Herz spaces, all the obtained results are new. The proofs of these results strongly depend on the properties of the kernel of T under consideration and also on the dual theorem on LX,q,s,d(ℝn).