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Conjugate Jacobi Series and Conjugate Functions

✍ Scribed by Zhongkai Li

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
509 KB
Volume
86
Category
Article
ISSN
0021-9045

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✦ Synopsis

Conjugate Jacobi series is introduced, according to the viewpoint of Muckenhoupt and Stein, in the sense that the Jacobi harmonic function and the conjugate harmonic function satisfy the generalized Cauchy Riemann equations. The integral form of Jacobi conjugate functions is also introduced, which is identifiable with the conjugate Jacobi series in some sense. The L 1 weak-boundedness and L p boundedness for 1< p< of the conjugacy mapping are proved. The convergence of the Abel means of conjugate Jacobi series is also considered.

1996 Academic Press, Inc. axis fixed. For *>0, consider the set [P * k (cos %)] of the ultraspherical polynomials, which is orthogonal over (0, ?) with respect to the measure sin 2* % d%. When 2* is integral, 2*=n&2, the P * k (cos %) arise in the Fourier article no.

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