On Hyper Singular Integral Operators over Weighted Sobolev Spaces

2009/08/17 by Dejenie A. Lakew, Lakew, Dejenie A.
Mathematics · #30G35 #35A22 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #math.FA #math.OA #msc:30G35 #msc:35A22

paper · pdf · doi:10.48550/arxiv.0908.2406

This article is about hyper singular integral operators defined over Sobolev spaces with weight. The weight on the volume measure is to control or eliminate exponents of singulaities caused by the integrands

arxiv created 2009/08/17 · openalex publication_date 2009/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study singular integral operators which are hyper or weak over Lipschitz or Holder spaces and over weghted Sobolev spaces defined on unbounded domains in the standard n-D space Rⁿ for n>0. The π-operator in this case is one of the hyper integral operators which has been studied extensively than other hyper singular integral operators. It will be shown the control of singularity of such integral operators that are defined interms of Cauchy generating kernels by working on weghted Sobolev spaces W^p,k(Ω,|x|^ζ+epsilondx) for some ε>0 and ζ some positive integer.

Related

• Analysis of hyper-singular, fractional, and order-zero singular integral\n operators
• On regularity and irregularity of certain holomorphic singular integral operators
• Cauchy singular integral operator with parameters in Log-Hölder spaces
• Singular integrals of non-convolution type on product spaces
• Integral operators on the Oshima compactification of a Riemannian symmetric space of non-compact type. Microlocal analysis and kernel asymptotics