Convergence of two-dimensional weighted integrals

Pramanik, Malabika

doi:10.1090/S0002-9947-01-02939-7

Convergence of two-dimensional weighted integrals

Author: Malabika Pramanik
Journal: Trans. Amer. Math. Soc. 354 (2002), 1651-1665
MSC (2000): Primary 42B10; Secondary 35S30, 41A60
DOI: https://doi.org/10.1090/S0002-9947-01-02939-7
Published electronically: November 21, 2001
MathSciNet review: 1873022
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A two-dimensional weighted integral in $\mathbb R^{2}$ is proposed as a tool for analyzing higher-dimensional unweighted integrals, and a necessary and sufficient condition for the finiteness of the weighted integral is obtained.

1. D. H. Phong and E. M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math. 179 (1997), no. 1, 105–152. MR 1484770, https://doi.org/10.1007/BF02392721
2. D.H. Phong, E.M. Stein, and J.A. Sturm, On the growth and stability of real-analytic functions, Amer. J. Math. 121 (1999), no. 3, 519-554. CMP 2000:07
3. S. Saks and A. Zygmund, Analytic functions, 3rd ed., Elsevier Publishing Co., Amsterdam-London-New York; PWN—Polish Scientific Publishers, Warsaw, 1971. Translated from the Polish by E. J. Scott. MR 0349963
4. C. L. Siegel, Topics in complex function theory. Vol. I: Elliptic functions and uniformization theory, Translated from the original German by A. Shenitzer and D. Solitar. Interscience Tracts in Pure and Applied Mathematics, No. 25, Wiley-Interscience A Division of John Wiley & Sons, New York-London-Sydney, 1969. MR 0257326
5. A. N. Varčenko, Newton polyhedra and estimates of oscillatory integrals, Funkcional. Anal. i Priložen. 10 (1976), no. 3, 13–38 (Russian). MR 0422257