CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

The Complete $(L^p,L^p)$ Mapping Properties of Some Oscillatory Integrals in Several Dimensions

  Published:2001-10-01
 Printed: Oct 2001
  • G. Sampson
  • P. Szeptycki
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We prove that the operators $\int_{\mathbb{R}_+^2} e^{ix^a \cdot y^b} \varphi (x,y) f(y)\, dy$ map $L^p(\mathbb{R}^2)$ into itself for $p \in J =\bigl[\frac{a_l+b_l}{a_l+(\frac{b_l r}{2})},\frac{a_l+b_l} {a_l(1-\frac{r}{2})}\bigr]$ if $a_l,b_l\ge 1$ and $\varphi(x,y)=|x-y|^{-r}$, $0\le r <2$, the result is sharp. Generalizations to dimensions $d>2$ are indicated.
MSC Classifications: 42B20, 46B70, 47G10 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Interpolation between normed linear spaces [See also 46M35]
Integral operators [See also 45P05]
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
46B70 - Interpolation between normed linear spaces [See also 46M35]
47G10 - Integral operators [See also 45P05]
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/