Geodesic
$L^p$ type mapping estimates for oscillatory integrals in higher dimensions
G. Sampson1
1 Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A.
Studia Mathematica, Tome 172 (2006) no. 2, pp. 101-123

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show in two dimensions that if $Kf=\int_{{\mathbb R}_+^2} k(x,y) f(y) \,dy$, $k(x,y)={e^{i x^a\cdot y^b}}/{|x-y|^{\eta}},$ $p={4}/{(2+\eta)}$, $a\ge b\ge \bar{1}=(1,1)$, $v_p(y)=y^{({p}/{p^{\prime}})(\bar{1}-b/a)}$, then $\|Kf\|_p\le C\|f\|_{p,v_p}$ if $\eta+\alpha_1+\alpha_22,$ $\alpha_j=1-{b_j}/{a_j}$, $j=1,2$. Our methods apply in all dimensions and also for more general kernels.
DOI : 10.4064/sm172-2-1
Keywords: dimensions int mathbb cdot x y eta eta bar prime bar b eta alpha alpha alpha methods apply dimensions general kernels

G. Sampson 1

1 Department of Mathematics Auburn University Auburn, AL 36849-5310, U.S.A. 
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G. Sampson. $L^p$ type mapping estimates for
 oscillatory integrals in higher dimensions. Studia Mathematica, Tome 172 (2006) no. 2, pp. 101-123. doi: 10.4064/sm172-2-1

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