Norm Inequalities for Integral Operators on Cones

2022/06/17 by Mohammad Vali Siadat, Siadat, Mohammad Vali
Mathematics · #4302 #4402 #4602 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.08987

openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this dissertation we explore the [L^p, L^q]-boundedness of certain integral operators on weighted spaces on cones in \mathbb Rⁿ. These integral operators are of the type ∫_Vk(x, y)f(y)dy defined on a homogeneous cone V. The results of this dissertation are then applied to an important class of operators such as Riemann-Liouville's fractional integral operators, Weyl's fractional integral operators and Laplace's operators. As special cases of the above, we obtain an \mathbb Rⁿ -generalization of the celebrated Hardy's inequality on domains of positivity. We also prove dual results.

Related

• Calculations of the norms for monotone operators on the cones of functions with monotonicity properties
• Riemann-Liouville and higher dimensional Harday operators for non-negative decreasing function in L^p(⋅) spaces
• A new approach to norm inequalities on weighted and variable Hardy\n spaces
• Boundedness and norm of certain p-adic Hardy-Littlewood-Pólya-type operators
• Criteria for boundedness of a class of integral operators from L_p to L_q for 1