Exceptional Sets of Slices for Functions From the Bergman Space in the Ball

2001 ◽  
Vol 44 (2) ◽  
pp. 150-159 ◽  
Author(s):  
Piotr Jakóbczak
Keyword(s):  
Unit Ball ◽  
Lebesgue Measure ◽  
Bergman Space ◽  
Dimensional Subspace ◽  
Natural Topology ◽  
Exceptional Set ◽  
One Dimensional ◽  
Exceptional Sets

AbstractLet BN be the unit ball in and let f be a function holomorphic and L2-integrable in BN. Denote by E(BN, f) the set of all slices of the form , where L is a complex one-dimensional subspace of , for which is not L2-integrable (with respect to the Lebesgue measure on L). Call this set the exceptional set for f. We give a characterization of exceptional sets which are closed in the natural topology of slices.

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

scholarly journals A characterization of weighted Bergman-Orlicz spaces on the unit ball in Cn

2003 ◽  
Vol 74 (1) ◽  
pp. 5-18 ◽  
Author(s):  
Yasuo Matsugu ◽  
Jun Miyazawa
Keyword(s):  
Convex Function ◽  
Unit Ball ◽  
Lebesgue Measure ◽  
Orlicz Space ◽  
Positive Constant ◽  
Real Line ◽  
Orlicz Spaces ◽  
Holomorphic Functions ◽  
Strongly Convex

AbstractLet B denote the unit ball in Cn, and ν the normalized Lebesgue measure on B. For α > −1, define Here cα is a positive constant such that να(B) = 1. Let H(B) denote the space of all holomorphic functions in B. For a twice differentiable, nondecreasing, nonnegative strongly convex function ϕ on the real line R, define the Bergman-Orlicz space Aϕ(να) by In this paper we prove that a function f ∈ H(B) is in Aϕ(να) if and only if where is the radial derivative of f.

Characterization of Minimum Route MTM in One-Dimensional Multi-Hop Wireless Networks

2009 ◽  
Vol E92-A (9) ◽  
pp. 2227-2235 ◽  
Author(s):  
Kazuyuki MIYAKITA ◽  
Keisuke NAKANO ◽  
Masakazu SENGOKU ◽  
Shoji SHINODA
Keyword(s):  
Wireless Networks ◽  
One Dimensional

Solvothermal Synthesis and Characterization of an One-Dimensional Zinc Phosphate

2002 ◽  
Vol 37 (2-3) ◽  
pp. 169-175 ◽  
Author(s):  
K. Yanxiong ◽  
L. Jianmin ◽  
Z. Yugen ◽  
H. Gaofei ◽  
J. Zheng ◽  
...  
Keyword(s):  
Solvothermal Synthesis ◽  
Zinc Phosphate ◽  
Synthesis And Characterization ◽  
One Dimensional

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals Synthesis and Structural Characterization of (E)-4-[(2-Hydroxy-3-methoxybenzylidene)amino]butanoic Acid and Its Novel Cu(II) Complex

Molbank ◽  
10.3390/m1179 ◽  
2021 ◽  
Vol 2021 (1) ◽  
pp. M1179
Author(s):  
Eleftherios Halevas ◽  
Antonios Hatzidimitriou ◽  
Barbara Mavroidi ◽  
Marina Sagnou ◽  
Maria Pelecanou ◽  
...  
Keyword(s):  
Schiff Base ◽  
Gamma Aminobutyric Acid ◽  
X Ray Diffraction ◽  
Reaction Conditions ◽  
Polymeric Compound ◽  
Bridging Ligands ◽  
1H And 13C Nmr ◽  
One Dimensional ◽  
Ft Ir

A novel Cu(II) complex based on the Schiff base obtained by the condensation of ortho-vanillin with gamma-aminobutyric acid was synthesized. The compounds are physico-chemically characterized by elemental analysis, HR-ESI-MS, FT-IR, and UV-Vis. The complex and the Schiff base ligand are further structurally identified by single crystal X-ray diffraction and 1H and 13C-NMR, respectively. The results suggest that the Schiff base are synthesized in excellent yield under mild reaction conditions in the presence of glacial acetic acid and the crystal structure of its Cu(II) complex reflects an one-dimensional polymeric compound. The molecular structure of the complex consists of a Cu(II) ion bound to two singly deprotonated Schiff base bridging ligands that form a CuN2O4 chelation environment, and a coordination sphere with a disordered octahedral geometry.

2D Self-assembly and Electronic Characterization of Oxygen-Boron-Oxygen-Doped Chiral Graphene Nanoribbons

2021 ◽  
Author(s):  
Lei Jin ◽  
Nerea Bilbao ◽  
Yang Lv ◽  
Xiao-Ye Wang ◽  
Soltani Paniz ◽  
...  
Keyword(s):  
Edge Effects ◽  
Self Assembly ◽  
Quantum Confinement ◽  
Graphene Nanoribbons ◽  
One Dimensional ◽  
The Past ◽  
Different Types

Graphene nanoribbons (GNRs), quasi-one-dimensional strips of graphene, exhibit a nonzero bandgap due to quantum confinement and edge effects. In the past decade, different types of GNRs with atomically precise structures...

ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ
Keyword(s):  
Entire Functions ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Numbers ◽  
Lecture Notes ◽  
Transcendental Entire Functions

In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

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