Displaying similar documents to “A Carleson inequality for B M O A functions with their derivatives on the unit ball”

Positive Toeplitz operators between the pluriharmonic Bergman spaces

Eun Sun Choi (2008)

Czechoslovak Mathematical Journal

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We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b p into another b q for 1 < p , q < ∞ in terms of certain Carleson and vanishing Carleson measures.

Dichotomies for 𝐂 0 ( X ) and 𝐂 b ( X ) spaces

Szymon Głąb, Filip Strobin (2013)

Czechoslovak Mathematical Journal

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Jachymski showed that the set ( x , y ) ∈ 𝐜 0 × 𝐜 0 : ∑ i = 1 n α ( i ) x ( i ) y ( i ) n = 1 ∞ is bounded is either a meager subset of 𝐜 0 × 𝐜 0 or is equal to 𝐜 0 × 𝐜 0 . In the paper we generalize this result by considering more general spaces than 𝐜 0 , namely 𝐂 0 ( X ) , the space of all continuous functions which vanish at infinity, and 𝐂 b ( X ) , the space of all continuous bounded functions. Moreover, we replace the meagerness by σ -porosity.

On the integral representation of superbiharmonic functions

Ali Abkar (2007)

Czechoslovak Mathematical Journal

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We consider a nonnegative superbiharmonic function w satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for w in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions w satisfying the condition 0 ≤ w ( z ) ≤ C ( 1 - | z | ) in the unit disk. As an application we shall see that the polynomials are dense in weighted...

On some problems connected with diagonal map in some spaces of analytic functions

Romi Shamoyan (2008)

Mathematica Bohemica

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For any holomorphic function f on the unit polydisk 𝔻 n we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag f ( z ) = f ( z , ... , z ) , and prove that the diagonal map Diag maps the space Q p , q , s ( 𝔻 n ) of the polydisk onto the space Q ^ p , s , n q ( 𝔻 ) of the unit disk.