$(L_p, L_q)$ estimates of potentials with oscillating kernel
| dc.creator | Ournycheva, E. | |
| dc.date | 2002-07-11 | |
| dc.date.accessioned | 2026-07-07T04:49:38Z | |
| dc.date.available | 2026-07-07T04:49:38Z | |
| dc.description | $(L_p, L_q)$ estimates are obtained for oscillatory potentials $(K^\alphaf)(x)=\int\limits_{R^n}\frac{\exp(i|y|)}{|y|^{n-α}}f(x-y)dy$, $0<α<n$, $n\geq 2$, 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 $(L_p, L_q)$ represents an open problem. The range of $α$ for which the problem is open is just the same as for the Bochner-Riesz means. | |
| dc.description | LaTex, 21 pages | |
| dc.identifier | https://arxiv.org/abs/math/0207095 | |
| dc.identifier | http://arxiv.org/abs/math/0207095 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64495 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | $(L_p, L_q)$ estimates of potentials with oscillating kernel | |
| dc.type | text |