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SPHERICAL NEWTON DISTANCE FOR OSCILLATORY INTEGRALS WITH HOMOGENEOUS PHASE FUNCTIONS
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  • Journal title : Honam Mathematical Journal
  • Volume 33, Issue 1,  2011, pp.1-9
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2011.33.1.001
 Title & Authors
SPHERICAL NEWTON DISTANCE FOR OSCILLATORY INTEGRALS WITH HOMOGENEOUS PHASE FUNCTIONS
Jo, Gyu-Dong; Lee, Sang-Hyun; Ryu, Chul-Woo; Suh, Young-Cha;
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 Abstract
In this paper we study oscillatory integrals with analytic homogeneous phase functions for smooth radial functions. We give their sharp asymptotic behavior in terms of spherical Newton distance.
 Keywords
oscillatory integral;homogeneous phase;spherical Newton distance;
 Language
English
 Cited by
 References
1.
M. Pramanik, C. W. Yang, Decay Estimate for Weighted Oscillatory Integrals in $R^2$. Indiana Univ. Math. J. 53 (2004), no.2, 613-645. crossref(new window)

2.
M. Pramanik, Convergence of two-dimensional weighted integrals. Trans. Amer. Math. Soc. 354 (2002), no.4, 1651-1665. crossref(new window)

3.
M. Pramanik, Weighted inequalities for real-analytic functions in $R^2$. Geom. Anal. 12 (2002), no.2, 265-288. crossref(new window)

4.
M. Greenblatt, A direct resolution of singularities for functions of two variables with applications to analysis. J. Anal. Math. 92 (2004), 233-257. crossref(new window)

5.
M. Greenblatt, Newton polygons and local integrability of negative powers of smooth functions in the plane. Trans. Amer. Math. Soc. 358 (2006), no.2, 657-670. crossref(new window)

6.
D. H. Phong, E. M. Stein, The Newton Polyhedon and oscillatory integral operators. Acta. Math. 179 (1997), no.1, 105-152. crossref(new window)

7.
D. H. Phong, E. M. Stein, J. Sturm, On the growth and stability of real-analytic functions. Amer. J. Math. 121 (1999), no.3, 519-554. crossref(new window)

8.
M. Greenblatt, The asymptotic behavior of degenerate oscillatory integrals in two dimensions. J. Funct. Anal. 257 (2009), no. 6, 1759-1798. crossref(new window)

9.
A. Varchenko, Newton polyhedron and estimation of oscillating integrals. Funct. Anal. Appl. 18 (1976), 175-196.

10.
W. Rudin., Real and complex analysis. McGraw-Hill Inc.(1987).