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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Convergence of two-dimensional weighted integrals
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by Malabika Pramanik
Trans. Amer. Math. Soc. 354 (2002), 1651-1665
DOI: https://doi.org/10.1090/S0002-9947-01-02939-7
Published electronically: November 21, 2001
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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.
References
  • D. H. Phong and E. M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math. 179 (1997), no. 1, 105–152. MR 1484770, DOI 10.1007/BF02392721
  • 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.
  • 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
  • C. L. Siegel, Topics in complex function theory. Vol. I: Elliptic functions and uniformization theory, Interscience Tracts in Pure and Applied Mathematics, No. 25, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1969. Translated from the original German by A. Shenitzer and D. Solitar. MR 0257326
  • A Varchenko, Newton polyhedron and estimation of oscillating integrals, Funct. Anal. Appl. 18 (1976), 175–196.
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Bibliographic Information
  • Malabika Pramanik
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 688168
  • ORCID: 0000-0003-1119-7534
  • Email: malabika@math.wisc.edu
  • Received by editor(s): October 16, 2000
  • Published electronically: November 21, 2001
  • Additional Notes: Research supported in part by NSF grant DMS-9970660
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1873022