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DOI QR Code

SPHERICAL NEWTON DISTANCE FOR OSCILLATORY INTEGRALS WITH HOMOGENEOUS PHASE FUNCTIONS

  • Received : 2010.04.07
  • Accepted : 2011.03.06
  • Published : 2011.03.25

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

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. https://doi.org/10.1512/iumj.2004.53.2388
  2. M. Pramanik, Convergence of two-dimensional weighted integrals. Trans. Amer. Math. Soc. 354 (2002), no.4, 1651-1665. https://doi.org/10.1090/S0002-9947-01-02939-7
  3. M. Pramanik, Weighted inequalities for real-analytic functions in $R^2$. Geom. Anal. 12 (2002), no.2, 265-288. https://doi.org/10.1007/BF02922043
  4. M. Greenblatt, A direct resolution of singularities for functions of two variables with applications to analysis. J. Anal. Math. 92 (2004), 233-257. https://doi.org/10.1007/BF02787763
  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. https://doi.org/10.1090/S0002-9947-05-03664-0
  6. D. H. Phong, E. M. Stein, The Newton Polyhedon and oscillatory integral operators. Acta. Math. 179 (1997), no.1, 105-152. https://doi.org/10.1007/BF02392721
  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. https://doi.org/10.1353/ajm.1999.0023
  8. M. Greenblatt, The asymptotic behavior of degenerate oscillatory integrals in two dimensions. J. Funct. Anal. 257 (2009), no. 6, 1759-1798. https://doi.org/10.1016/j.jfa.2009.06.015
  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).