In this paper we prove a number of sharp results on the permissible growth of derivatives of multipliers of fractional Cauchy transforms. For example, we prove that if f g M then there exists a positive constant C such that H M 1 1yr 1qlog 1r 1 y r Ž . Ž . y w . for r g 0, 1 . This result is proved
Generalized Multipliers of Families of Cauchy Transforms
✍ Scribed by R.A. Hibschweiler
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 381 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
The ranges of Mellin multiplier transformations are considered when the multiplier has zeros. Applications are made to Bilateral Laplace and Fourier multiplier transformations.
## Abstract In this paper, we study the growth behaviour of entire Clifford algebra‐valued solutions to iterated Dirac and generalized Cauchy–Riemann equations in higher‐dimensional Euclidean space. Solutions to this type of systems of partial differential equations are often called __k__‐monogenic
## Abstract We define and investigate the multipliers of Laplace transform type associated to the differential operator __L~λ~f__ (__θ__) = –__f__ ″(__θ__) – 2__λ__ cot __θf__ ′(__θ__) + __λ__^2^__f__ (__θ__), __λ__ > 0. We prove that these operators are bounded in __L^p^__ ((0, __π__), __dm~λ~__)