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Fourier multipliers on weighted  -spaces
Author(s):
T.
S.
Quek
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2343-2351.
MSC (1991):
Primary 42A45
Posted:
April 9, 1999
MathSciNet review:
1486747
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Abstract:
In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type  on  if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery's result is sharp in a certain sense. We also obtain a weighted analogue of Carbery's result. Some applications of our results are also given.
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Additional Information:
T.
S.
Quek
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119260, Republic of Singapore
Email:
matqts@leonis.nus.edu.sg
DOI:
10.1090/S0002-9939-99-04812-1
PII:
S 0002-9939(99)04812-1
Keywords:
Singular integral operators,
Fourier multipliers,
weighted $L^{p}$-spaces
Received by editor(s):
August 20, 1996
Received by editor(s) in revised form:
October 31, 1997
Posted:
April 9, 1999
Dedicated:
Dedicated to Professor Leonard Y. H. Yap on the ocassion of his sixtieth birthday
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1999,
American Mathematical Society
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