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On some spaces of holomorphic functions of exponential growth on a half-plane

Marco M. Peloso, Maura Salvatori (2016)

Concrete Operators

In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...

On the characteristic properties of certain optimization problems in complex analysis

Józef Baranowicz, Leon Mikołajczyk (1995)

Banach Center Publications

We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces S ¹ α and S ₁ α for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

On the powers of quasihomogeneous Toeplitz operators

Aissa Bouhali, Zohra Bendaoud, Issam Louhichi (2021)

Czechoslovak Mathematical Journal

We present sufficient conditions for the existence of p th powers of a quasihomogeneous Toeplitz operator T e i s θ ψ , where ψ is a radial polynomial function and p , s are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.

On the Product of Functions in BMO and H 1

Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister (2007)

Annales de l’institut Fourier

The point-wise product of a function of bounded mean oscillation with a function of the Hardy space H 1 is not locally integrable in general. However, in view of the duality between H 1 and B M O , we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic...

On the weighted estimate of the Bergman projection

Benoît Florent Sehba (2018)

Czechoslovak Mathematical Journal

We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.

On Volterra composition operators from Bergman-type space to Bloch-type space

Zhi Jie Jiang (2011)

Czechoslovak Mathematical Journal

Let ϕ be an analytic self-mapping of 𝔻 and g an analytic function on 𝔻 . In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols g and ϕ .

On weighted composition operators acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces

Elke Wolf (2011)

Annales Polonici Mathematici

Let ϕ: → and ψ: → ℂ be analytic maps. They induce a weighted composition operator ψ C ϕ acting between weighted Bergman spaces of infinite order and weighted Bloch type spaces. Under some assumptions on the weights we give a characterization for such an operator to be bounded in terms of the weights involved as well as the functions ψ and ϕ

On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky, Khim R. Shrestha (2015)

Banach Center Publications

In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces H u p . We also provide a reduction of H ∞ problems to H u p problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

On weighted spaces of functions harmonic in ℝ n

Albert I. Petrosyan (2006)

Commentationes Mathematicae Universitatis Carolinae

The paper establishes integral representation formulas in arbitrarily wide Banach spaces b ω p ( ℝ n ) of functions harmonic in the whole ℝ n .

Outers for noncommutative H p revisited

David P. Blecher, Louis E. Labuschagne (2013)

Studia Mathematica

We continue our study of outer elements of the noncommutative H p spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in H p actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...

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