On the framework of L_p summations for functions

2021/08/16 by Michae Roysdon, Roysdon, Michae, Sudan Xing +1 · 1 citation
Computer Science · Mathematics · #2010 Mathematics Subject Classification.Primary: 52A39 #26D15 #46N10 #52A40 #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #Secondary: 28A75

paper · pdf · doi:10.48550/arxiv.2108.06929

openalex publication_date 2021/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the framework of L_p operations for functions by introducing two primary new types L_p,s summations for p>0: the L_p,s convolution sum and the L_p,s Asplund sum for functions. The first type is defined as the linear summations of functions in terms of the L_p coefficients (C_p,λ,t, D_p,λ,t), the so-called the L_p,s supremal-convolution when p≥1 and the L_p,s inf-sup-convolution when 0

Cited by

• Functional Liftings of Restricted Geometric Inequalities

Related

• Poisson summation formulas: A new approach
• Poisson summation formula in weighted Lebesgue spaces
• Estimates of convolution operators of functions from L_2π^p(x)
• Summability Kernels for L^p Multipliers
• Involves averaging arithmetic and integral partial functions over sparse set