Abstract: 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 \(\cal{L}\)-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 \(\mathbb{R}^n\).
For citation: Gurov M. N., Nogin V. A. \(L_p-L_q\)-estimates for generalized Riss potentials with oscillating kernels.Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 3-10. DOI 10.23671/VNC.2017.2.6503
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