Geodesic
$L_p-L_q$-estimates for generalized Riss potentials with oscillating
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 2, pp. 3-10 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a class of multidimensional potential-type operators whose kernels are oscillating at infinity. The characteristics of these operators are infinitely differentiable homogeneous functions. We describe convex sets in the $(1/p;1/q)$-plane for which these operators are bounded from $L_p$ into $L_q$ and indicate the domains where they are not bounded. In some cases we describe their $\mathcal{L}$-characteristics. To obtain these results we use a new method based on special representation of the symbols of multidimensional potential-type operators. To these representations of the symbols we apply the technique of Fourier-multipliers, which degenerate or have singularities on the unit sphere in $\mathbb{R}^n$. 
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M. N. Gurov; V. A. Nogin. $L_p-L_q$-estimates for generalized Riss potentials with oscillating. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 2, pp. 3-10. http://geodesic.mathdoc.fr/item/VMJ_2017_19_2_a0/

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