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On pasting  -weights
Author(s):
Bernd
S. W.
Schröder
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3339-3344.
MSC (1991):
Primary 26D07, 28A25, 42A20, 47B99
MathSciNet review:
1328376
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Abstract:
Theorem 3 gives a condition when two  -weights can be ``pasted'' together to yield another  -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.
References:
- [BS1]
- A. Böttcher and I. Spitkovsky, Wiener-Hopf integral operators with PC symbols on spaces with Muckenhoupt weight, Rev. Mat. Iberoamericana 9 (1993), 257--279. MR 94e:45004
- [BS2]
- ------, On a theorem of Rooney concerning the spectrum of the singular integral operator, Z. Anal. Anwendungen 12 (1993), 93--96. MR 94h:47093
- [CU]
- D. Cruz-Uribe, Piecewise monotonic doubling measures, Ph. D. dissertation.
- [GKS]
- I. Gohberg, N. Krupnik, I. Spitkovsky, Banach algebras of singular integral operators with piecewise continuous coefficients. General contour and weight, Integral Equations Operator Theory 17 (1993), 322--337. MR 94f:47057
- [HMW]
- R. Hunt, B. Muckenhoupt, R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans.Amer. Math. Soc. 176 (1973), 227--251. MR 47:701
- [JN]
- R. Johnson, C. Neugebauer, Change of variable results for
 -and reverse Hölder  -classes, Trans. Amer. Math. Soc. 328 (1991), 639--666. MR 92c:42019 - [Sp]
- I. Spitkovsky, Singular integral operators with PC symbols on the spaces with general weights, J. Funct. Anal. 105 (1992), 129--143. MR 93d:47057
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Additional Information:
Bernd
S. W.
Schröder
Affiliation:
Department of Mathematics, Hampton University, Hampton, Virginia 23668
Email:
schroder@huajai.cs.hamptonu.edu
DOI:
10.1090/S0002-9939-96-03421-1
PII:
S 0002-9939(96)03421-1
Keywords:
$A_p$-weight,
pasting,
contour,
Fourier series,
Hilbert transform,
Cauchy operator
Received by editor(s):
September 14, 1994
Received by editor(s) in revised form:
March 25, 1995
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1996,
American Mathematical Society
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