scholarly journals Characterization of Carleson measures by the Hausdorff-Young property

2013 ◽  
Vol 94 (3-4) ◽  
pp. 551-558 ◽  
Author(s):  
S. Yu. Sadov
Keyword(s):  
Carleson Measures

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.

Carleson measure characterizations of the Campanato type space associated with Schrödinger operators on stratified Lie groups

2020 ◽  
Vol 32 (5) ◽  
pp. 1337-1373 ◽  
Author(s):  
Yixin Wang ◽  
Yu Liu ◽  
Chuanhong Sun ◽  
Pengtao Li
Keyword(s):  
Carleson Measures ◽  
Heat Semigroup ◽  
Stratified Lie Group ◽  
Poisson Semigroup ◽  
Homogeneous Dimension ◽  
Type Spaces ◽  
Stratified Lie Groups ◽  
Lusin Area Function ◽  
Reverse Hölder

AbstractLet {\mathcal{L}=-{\Delta}_{\mathbb{G}}+V} be a Schrödinger operator on the stratified Lie group {\mathbb{G}}, where {{\Delta}_{\mathbb{G}}} is the sub-Laplacian and the nonnegative potential V belongs to the reverse Hölder class {B_{q_{0}}} with {q_{0}>\mathcal{Q}/2} and {\mathcal{Q}} is the homogeneous dimension of {\mathbb{G}}. In this article, by Campanato type spaces {\Lambda^{\alpha}_{\mathcal{L}}(\mathbb{G})}, we introduce Hardy type spaces associated with {\mathcal{L}} denoted by {H^{{p}}_{\vphantom{\varepsilon}{\mathcal{L}}}(\mathbb{G})} and prove the atomic characterization of {H^{{p}}_{\vphantom{\varepsilon}{\mathcal{L}}}(\mathbb{G})}. Further, we obtain the following duality relation:\Lambda_{\mathcal{L}}^{\mathcal{Q}(1/p-1)}(\mathbb{G})=(H^{{p}}_{\vphantom{% \varepsilon}{\mathcal{L}}}(\mathbb{G}))^{\ast},\quad\mathcal{Q}/(\mathcal{Q}+% \delta)<p<1\quad\text{for}\ \delta=\min\{1,2-\mathcal{Q}/q_{0}\}.The above relation enables us to characterize {\Lambda^{\alpha}_{\mathcal{L}}(\mathbb{G})} via two families of Carleson measures generated by the heat semigroup and the Poisson semigroup, respectively. Also, we obtain two classes of perturbation formulas associated with the semigroups related to {\mathcal{L}}. As applications, we obtain the boundedness of the Littlewood–Paley function and the Lusin area function on {\Lambda^{\alpha}_{\mathcal{L}}(\mathbb{G})}.

scholarly journals Compact differences of weighted composition operators

2020 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä
Keyword(s):  
Bergman Space ◽  
Composition Operators ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Weighted Composition Operators ◽  
Doubling Weights ◽  
Weighted Composition ◽  
The Way

AbstractCompact differences of two weighted composition operators acting from the weighted Bergman space $$A^p_{\omega }$$ A ω p to another weighted Bergman space $$A^q_{\nu }$$ A ν q , where $$0<p\le q<\infty $$ 0 < p ≤ q < ∞ and $$\omega ,\nu $$ ω , ν belong to the class $${\mathcal {D}}$$ D of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for $$A^p_{\omega }$$ A ω p , with $$\omega \in {\mathcal {D}}$$ ω ∈ D , in terms of 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.

scholarly journals -Carleson Measures for a Class of Hardy-Orlicz Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Benoît Florent Sehba
Keyword(s):  
Composition Operators ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Alternative Interpretation ◽  
Carleson Measures ◽  
Weighted Composition Operators ◽  
Weak Factorization ◽  
Type Integral ◽  
Weighted Composition

An alternative interpretation of a family of weighted Carleson measures is used to characterize -Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic function spaces.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

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