On the weak (1,1) boundedness of a class of oscillatory singular integrals

Yibiao Pan

Studia Mathematica (1993)

  • Volume: 106, Issue: 3, page 279-287
  • ISSN: 0039-3223

Abstract

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We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include ϕ ( x ) = e - 1 / x 2 and ϕ ( x ) = x e - 1 / | x | . Some related counterexample is also discussed.

How to cite

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Pan, Yibiao. "On the weak (1,1) boundedness of a class of oscillatory singular integrals." Studia Mathematica 106.3 (1993): 279-287. <http://eudml.org/doc/216017>.

@article{Pan1993,
abstract = {We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include $ϕ(x) = e^\{-1/x^2\}$ and $ϕ(x) = xe^\{-1/|x|\}$. Some related counterexample is also discussed.},
author = {Pan, Yibiao},
journal = {Studia Mathematica},
keywords = {weak (1,1) boundedness; oscillatory singular integrals; phase functions},
language = {eng},
number = {3},
pages = {279-287},
title = {On the weak (1,1) boundedness of a class of oscillatory singular integrals},
url = {http://eudml.org/doc/216017},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Pan, Yibiao
TI - On the weak (1,1) boundedness of a class of oscillatory singular integrals
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 3
SP - 279
EP - 287
AB - We prove the uniform weak (1,1) boundedness of a class of oscillatory singular integrals under certain conditions on the phase functions. Our conditions allow the phase function to be completely flat. Examples of such phase functions include $ϕ(x) = e^{-1/x^2}$ and $ϕ(x) = xe^{-1/|x|}$. Some related counterexample is also discussed.
LA - eng
KW - weak (1,1) boundedness; oscillatory singular integrals; phase functions
UR - http://eudml.org/doc/216017
ER -

References

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