Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo-Differential Operators

2025/02/18 by Un Ji, Ji, Un Cig, Jae Hun Kim +1
Mathematics · Computer Science · Engineering · #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2502.12588

Abstract

In this paper, we first prove that the kernel of convolution operator, corresponding the composition of pseudo-differential operator and evolution system associated with the symbol depending on time, satisfies the Hörmander's condition. Secondly, we prove that the convolution operator is a bounded linear operator from the Besov space on ℝ^d into L^q(ℝ^d;V) for a Banach space V. Finally, by applying the Calderón-Zygmund theorem for vector-valued functions, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators.

Related

• A Generalization of Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo Differential Operators
• A pseudodifferential Hormander's inequality
• Sharp estimates for pseudo-differential operators of type (1,1) on\n Triebel-Lizorkin and Besov spaces
• An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
• Sharp maximal function estimates and H^p continuities of pseudo-differential operators