scholarly journals Regularity on the boundary in spaces of holomorphic functions on the unit disk

2010 ◽  
pp. 91-119 ◽  
Author(s):  
Emmanuel Fricain ◽  
Andreas Hartmann
Keyword(s):  
Unit Disk ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions

Disjointness of composition operators on Hv0 spaces

2020 ◽  
Vol 70 (6) ◽  
pp. 1357-1366
Author(s):  
Yu-Xia Liang ◽  
Ze-Hua Zhou
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Banach Spaces

AbstractThe disjoint properties of finitely many composition operators acting on the weighted Banach spaces of holomorphic functions in the unit disk were investigated in this paper.

scholarly journals Green's formula and the Hardy-Stein identities

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 135-153 ◽  
Author(s):  
Miroslav Pavlovic
Keyword(s):  
New York ◽  
Hardy Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Hardy Spaces ◽  
London Math ◽  
Analogous Result ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Complex Ball

This is a collection of some known and some new facts on the holomorphic and the harmonic version of the Hardy-Stein identity as well as on their extensions to the real and the complex ball. For example, we prove that if f is holomorphic on the unit disk D, then ??f ??Hp = ?f(0)?p + ?D?f'(z)? p-2 ?f'(z)?2(1-?z?) dA(z), (?) where Hp is the p-Hardy space, which improves a result of Yamashita [Proc. Amer. Math. Soc. 75 (1979), no. 1, 69-72]. An extension of (?) to the unit ball of Cn improves results of Beatrous an Burbea [Kodai Math. J. 8 (1985), 36-51], and of Stoll [J. London Math. Soc. (2) 48 (1993), no. 1, 126-136]. We also prove the analogous result for the harmonic Hardy spaces. The proofs of known results are shorter and more elementary then the existing ones, see Zhu [Spaces of holomorphic functions in the unit ball, Graduate Texts in Mathematics, vol. 226, Springer-Verlag, New York, 2005, Ch. IV]. We correct some constants in that book and in a paper of Jevtic and Pavlovic [Publ. Inst. Math. (Beograd) (N.S.) 64(78) (1998), 36-52].

scholarly journals Toeplitz operators on weighted spaces of holomorphic functions

2008 ◽  
Vol 103 (1) ◽  
pp. 40 ◽  
Author(s):  
Anahit Harutyunyan ◽  
Wolfgang Lusky
Keyword(s):  
Toeplitz Operator ◽  
Unit Disk ◽  
Essential Spectrum ◽  
Complex Plane ◽  
Toeplitz Operators ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Norm Estimates ◽  
Spaces Of Holomorphic Functions

We define a notion of Toeplitz operator on certain spaces of holomorphic functions on the unit disk and on the complex plane which are endowed with a weighted sup-norm. We establish boundedness and compactness conditions, give norm estimates and characterize the essential spectrum of these operators for many symbols.

scholarly journals Differences of Composition Operators Followed by Differentiation between Weighted Banach Spaces of Holomorphic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Cui Chen ◽  
Ren-Yu Chen ◽  
Ze-Hua Zhou
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Type Spaces ◽  
Weighted Banach Spaces

We characterize the boundedness and compactness of differences of the composition operators followed by differentiation between weighted Banach spaces of holomorphic functions in the unit disk. As their corollaries, some related results on the differences of composition operators acting from weighted Banach spaces to weighted Bloch type spaces are also obtained.

scholarly journals DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS

2010 ◽  
Vol 52 (2) ◽  
pp. 325-332 ◽  
Author(s):  
ELKE WOLF
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Open Unit Disk ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Banach Spaces

AbstractWe characterise boundedness and compactness of differences of composition operators acting between weighted Bergman spaces Av, p and weighted Banach spaces H∞w of holomorphic functions defined on the open unit disk D.

scholarly journals Coefficients problems for families of holomorphic functions related to hyperbola

2020 ◽  
Vol 70 (3) ◽  
pp. 605-616
Author(s):  
Stanisława Kanas ◽  
Vali Soltani Masih ◽  
Ali Ebadian
Keyword(s):  
Unit Disk ◽  
Holomorphic Functions ◽  
Hankel Determinant ◽  
Coefficient Problem

AbstractWe consider a family of analytic and normalized functions that are related to the domains ℍ(s), with a right branch of a hyperbolas H(s) as a boundary. The hyperbola H(s) is given by the relation $\begin{array}{} \frac{1}{\rho}=\left( 2\cos\frac{\varphi}{s}\right)^s\quad (0 \lt s\le 1,\, |\varphi| \lt (\pi s)/2). \end{array}$ We mainly study a coefficient problem of the families of functions for which zf′/f or 1 + zf″/f′ map the unit disk onto a subset of ℍ(s) . We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.

scholarly journals Traces of certain classes of holomorphic functions on finite unions of Carleson sequences

1999 ◽  
Vol 41 (1) ◽  
pp. 103-114 ◽  
Author(s):  
ANDREAS HARTMANN
Keyword(s):  
Holomorphic Functions ◽  
Spaces Of Holomorphic Functions ◽  
Hardy Classes ◽  
Type Spaces ◽  
Trace Spaces

We give a method allowing the generalization of the description of trace spaces of certain classes of holomorphic functions on Carleson sequences to finite unions of Carleson sequences. We apply the result to different classes of spaces of holomorphic functions such as Hardy classes and Bergman type spaces.

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