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Search: All articles in the CMB digital archive with keyword Hardy spaces

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1. CMB 2011 (vol 56 pp. 229)

Arvanitidis, Athanasios G.; Siskakis, Aristomenis G.
Cesàro Operators on the Hardy Spaces of the Half-Plane
In this article we study the Cesàro operator $$ \mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta, $$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also discussed.

Keywords:Cesàro operators, Hardy spaces, semigroups, composition operators
Categories:47B38, 30H10, 47D03

2. CMB 2011 (vol 55 pp. 303)

Han, Yongsheng; Lee, Ming-Yi; Lin, Chin-Cheng
Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces
In this article, we establish a new atomic decomposition for $f\in L^2_w\cap H^p_w$, where the decomposition converges in $L^2_w$-norm rather than in the distribution sense. As applications of this decomposition, assuming that $T$ is a linear operator bounded on $L^2_w$ and $0
Keywords:$A_p$ weights, atomic decomposition, Calderón reproducing formula, weighted Hardy spaces
Categories:42B25, 42B30

3. CMB 2010 (vol 54 pp. 159)

Sababheh, Mohammad
Hardy Inequalities on the Real Line
We prove that some inequalities, which are considered to be generalizations of Hardy's inequality on the circle, can be modified and proved to be true for functions integrable on the real line. In fact we would like to show that some constructions that were used to prove the Littlewood conjecture can be used similarly to produce real Hardy-type inequalities. This discussion will lead to many questions concerning the relationship between Hardy-type inequalities on the circle and those on the real line.

Keywords:Hardy's inequality, inequalities including the Fourier transform and Hardy spaces
Categories:42A05, 42A99

4. CMB 2006 (vol 49 pp. 381)

Girela, Daniel; Peláez, José Ángel
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain
It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces $A^p$ with $01$). As a consequence, we prove that there exists a Blaschke product $B$ with zeros on a radius such that $B'\notin A^{3/2}$.

Keywords:Blaschke products, Hardy spaces, Bergman spaces
Categories:30D50, 30D55, 32A36

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