Abstract
For the operator Aα with symbol |ξ|−α e i|ξ|,n-1/2 < α < n the description of the set of pairs ( 1/p, 1/q) for which it is bounded from L p into L q is given. As am application, the operators with symbols ω(ξ′)|ξ|−α e iγ|ξ| where ω(ξ′) is a homogeneous function of degree zero, γ > 0, are also considered.
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Karapetyants, A., Nogin, V.A. On ℒ Characteristic of Some Potential Type Operators with Oscillating Symbols and Singularities of the Kernels on a Sphere. Acta Mathematica Hungarica 92, 1–10 (2001). https://doi.org/10.1023/A:1013772408135
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DOI: https://doi.org/10.1023/A:1013772408135