(Lₚ, Lq) estimates of potentials with oscillating kernel
Ournycheva, E.
Original · EN
(Lₚ, Lq) estimates are obtained for oscillatory potentials (K)(x)=∫ᵣₙ(i|y|)|y|ⁿ⁻αf(x-y)dy, 0<α<n, n≥ 2, whose symbol has a singularity on the unit sphere. These potentials are natural modifications of the celebrated Bochner-Riesz operator and Helmholtz potential arising in Fourier analysis and PDE. For some values of α, determination of the corresponding pairs (Lₚ, Lq) represents an open problem. The range of α for which the problem is open is just the same as for the Bochner-Riesz means.
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