Fractional Cauchy Transforms

2020 ◽  
Author(s):  
Rita A. Hibschweiler ◽  
Thomas H. MacGregor
Keyword(s):  
Cauchy Transforms

scholarly journals Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains

2006 ◽  
Vol 82 (9) ◽  
pp. 167-172
Author(s):  
Eisuke Imamura ◽  
Kiyosato Okamoto ◽  
Michiroh Tsukamoto ◽  
Atsushi Yamamori
Keyword(s):  
Generalized Poisson ◽  
Cauchy Transforms

scholarly journals Products of Composition and Differentiation between the Fractional Cauchy Spaces and the Bloch-Type Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
R. A. Hibschweiler
Keyword(s):  
Unit Disc ◽  
Cauchy Transforms ◽  
Type Spaces ◽  
Cauchy Spaces

The operators D C Φ and C Φ D are defined by D C Φ f = f ∘ Φ ′ and C Φ D f = f ′ ∘ Φ where Φ is an analytic self-map of the unit disc and f is analytic in the disc. A characterization is provided for boundedness and compactness of the products of composition and differentiation from the spaces of fractional Cauchy transforms F α to the Bloch-type spaces B β , where α > 0 and β > 0 . In the case β < 2 , the operator D C Φ : F α ⟶ B β is compact ⇔ D C Φ : F α ⟶ B β is bounded ⇔ Φ ′ ∈ B β , Φ Φ ′ ∈ B β and Φ ∞ < 1 . For β < 1 , C Φ D : F α ⟶ B β is compact ⇔ C Φ D : F α ⟶ B β is bounded ⇔ Φ ∈ B β and Φ ∞ < 1 .

scholarly journals On Properties of Multipliers of Cauchy Transforms

1998 ◽  
Vol 28 (1) ◽  
pp. 223-235 ◽  
Author(s):  
D.J. Hallenbeck ◽  
K. Samotij
Keyword(s):  
Cauchy Transforms

scholarly journals Cauchy transforms of point masses: The logarithmic derivative of polynomials

2006 ◽  
Vol 163 (3) ◽  
pp. 1057-1076 ◽  
Author(s):  
J. Anderson ◽  
Vladimir Eiderman
Keyword(s):  
Logarithmic Derivative ◽  
Cauchy Transforms

Other operators on the Cauchy transforms

2006 ◽  
pp. 249-253
Author(s):  
Joseph Cima ◽  
Alec Matheson ◽  
William Ross
Keyword(s):  
Cauchy Transforms

Multipliers of Fractional Cauchy Transforms and Smoothness Conditions

1998 ◽  
Vol 50 (3) ◽  
pp. 595-604 ◽  
Author(s):  
Donghan Luo ◽  
Thomas Macgregor
Keyword(s):  
Analytic Function ◽  
Unit Circle ◽  
Unit Disk ◽  
Borel Measure ◽  
Open Unit ◽  
Open Unit Disk ◽  
Cauchy Transforms ◽  
The Family ◽  
Complex Borel Measure

AbstractThis paper studies conditions on an analytic function that imply it belongs to Mα, the set of multipliers of the family of functions given by where μ is a complex Borel measure on the unit circle and α > 0. There are two main theorems. The first asserts that if 0 < α < 1 and sup. The second asserts that if 0 < α < 1, ƒ ∈ H∞ and supt. The conditions in these theorems are shown to relate to a number of smoothness conditions on the unit circle for a function analytic in the open unit disk and continuous in its closure.

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