Communications in Mathematical Analysis

$L^2$-estimates for the Laplace transform along a family of hyperbolas in the right half-plane

Anatoli Merzon and Sergey Sadov

Full-text: Open access

Abstract

By Paley-Wiener theory, the Laplace transform of an $L^2$ function on positive semiaxis satisfies $L^2$ estimates uniformly on the family of vertical lines in the right half-plane. The paper gives a generalization: uniform $L^2$ estimates for the Laplace transform remain valid on a family of hyperbolas in the right half-plane.

Article information

Source
Commun. Math. Anal., Conference 3 (2011), 204-208.

Dates
First available in Project Euclid: 25 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.cma/1298670013

Mathematical Reviews number (MathSciNet)
MR2772062

Zentralblatt MATH identifier
1209.44001

Subjects
Primary: 44A10: Laplace transform

Keywords
Laplace transform $L^2$ estimates hyperbola Paley-Wiener theory Poisson integral

Citation

Sadov, Sergey; Merzon, Anatoli. $L^2$-estimates for the Laplace transform along a family of hyperbolas in the right half-plane. Commun. Math. Anal. (2011), no. 3, 204--208. https://projecteuclid.org/euclid.cma/1298670013


Export citation

References

  • J. Bergh and J. Löfström, Interpolation Spaces. An introduction. Springer, 1976.
  • L. Grafakos, Classical and Modern Fourier Analysis. Pearson Education Inc., 2004.
  • G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities. Cambridge Univ. Press, 1934.
  • E. Hille, Analytic Function Theory. Vol. II. Chelsea Pub. Co., 1973.
  • R. C. Paley and N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc., 1934.
  • P. Zhevandrov and A. Merzon, On the Neumann problem for the Helmholtz equation in a plane angle. Mathematical Methods in the Applied Sciences 23 (2000), pp 1401-1446.