Journal of Integral Equations and Applications

The compactness of a weakly singular integral operator on weighted Sobolev spaces

David Elliott

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It is shown that the weakly singular integral operator~$\int_{-1}^{1}\big(\phi(\tau)/|\tau -t|^{\gamma}\big)\,d\tau$, where $0\lt \gamma\lt 1$, maps the weighted Sobolev space~$W_{p;\alpha,\beta}^{(n)}(\Omega)$ compactly into itself for $1\lt p\lt \infty$, $0\lt \alpha+1/q, \beta+1/q\lt 1$~and $n\in \mathbb{N}_0$.

Article information

J. Integral Equations Applications, Volume 26, Number 4 (2014), 483-496.

First available in Project Euclid: 9 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)


Elliott, David. The compactness of a weakly singular integral operator on weighted Sobolev spaces. J. Integral Equations Applications 26 (2014), no. 4, 483--496. doi:10.1216/JIE-2014-26-4-483.

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