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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)...

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

Alexander V. Abanin, Pham Trong Tien (2012)

Studia Mathematica

We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane, Imed Feki (2014)

Czechoslovak Mathematical Journal

We prove some optimal logarithmic estimates in the Hardy space H ∞ ( G ) with Hölder regularity, where G is the open unit disk or an annular domain of ℂ . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space H k , ∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...

Polyanalytic Besov spaces and approximation by dilatations

Ali Abkar (2024)

Czechoslovak Mathematical Journal

Using partial derivatives ∂ f / ∂ z and ∂ f / ∂ z ¯ , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree q can be approximated in norm by polyanalytic polynomials of degree at most q .

Products of Toeplitz operators and Hankel operators

Yufeng Lu, Linghui Kong (2014)

Studia Mathematica

We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.

Properties of harmonic conjugates

Paweł Sobolewski (2008)

Annales UMCS, Mathematica

We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.

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