The Schur sufficiency condition for boundedness of any integral operator with non-negative kernel between L 2 -spaces is deduced from an observation, Proposition 1.2, about the central role played by L 2 -spaces in the general theory of these operators. Suppose (0, M, +) is a measure space and that
✦ LIBER ✦
On Integral Operators of Wiener-Hopf Type with Piecewise Difference Kernels
✍ Scribed by B.A. Kon
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 211 KB
- Volume
- 185
- Category
- Article
- ISSN
- 0022-247X
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## Abstract We consider a class of multidimensional potential‐type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/__p,__ 1/__q__)‐plane for which these operators are bounded from __L~p~