Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



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
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.

References [Enhancements On Off] (What's this?)

  • 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
  • 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, 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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 42B10, 35S30, 41A60

Retrieve articles in all journals with MSC (2000): 42B10, 35S30, 41A60

Additional Information

Malabika Pramanik
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
MR Author ID: 688168
ORCID: 0000-0003-1119-7534

Keywords: Harmonic analysis, weighted integrals
Received by editor(s): October 16, 2000
Published electronically: November 21, 2001
Additional Notes: Research supported in part by NSF grant DMS-9970660
Article copyright: © Copyright 2001 American Mathematical Society