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Sobolev Type Spaces Associated with Bessel Operators

✍ Scribed by Ram S. Pathak; Pradip K. Pandey

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
223 KB
Volume
215
Category
Article
ISSN
0022-247X

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✦ Synopsis

A Sobolev type space G s, p is defined and its properties including completeness and inclusion are investigated using the theory of distributional Hankel transform. The Hankel potential H s is defined. It is shown that the Hankel potential H s is a continuous linear mapping of the Zemanian space H into itself. The L p -space of s, p Ž . s,p all such Hankel potentials, W 0, ϱ is defined. It is shown that W is a 5 5 Banach space with respect to the norm . It is also shown that the Hankel s, p, potential is an isometry of W s, p . An L p -boundedness result for the Hankel potential is proved. It is shown that solutions of certain nonhomogeneous equations involving Bessel differential operators belong to these spaces. ᮊ 1997 Aca- demic Press

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## Abstract Properties of integral operators with weak singularities arc investigated. It is assumed that __G__ ⊂ ℝ^n^ is a bounded domain. The boundary δ__G__ should be smooth concerning the Sobolev trace theorem. It will be proved that the integral operators \documentclass{article}\pagestyle{empt