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
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Abstract | References | Similar Articles | Additional Information
Abstract: A two-dimensional weighted integral in 
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.
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- 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, Elsevier, Amsterdam-London-New York, 1971. MR 50:2456
- 4. C. L. Siegel, Topics in Complex Function Theory, vol. 1, Wiley-Interscience, New York, 1969. MR 41:1977
- 5. A Varchenko, Newton polyhedron and estimation of oscillating integrals, Funct. Anal. Appl. 18 (1976), 175-196. MR 54:10248
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Additional Information
Malabika Pramanik
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
malabika@math.wisc.edu
DOI:
https://doi.org/10.1090/S0002-9947-01-02939-7
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
