On pasting -weights

Author:
Bernd S. W. Schröder

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3339-3344

MSC (1991):
Primary 26D07, 28A25, 42A20, 47B99

DOI:
https://doi.org/10.1090/S0002-9939-96-03421-1

MathSciNet review:
1328376

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Abstract | References | Similar Articles | Additional Information

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.

**[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:
https://doi.org/10.1090/S0002-9939-96-03421-1

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

Article copyright:
© Copyright 1996
American Mathematical Society