Displaying similar documents to “On some problems connected with diagonal map in some spaces of analytic functions”

Norm and Taylor coefficients estimates of holomorphic functions in balls

Jacob Burbeam, Do Young Kwak (1991)

Annales Polonici Mathematici

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A classical result of Hardy and Littlewood states that if f ( z ) = ∑ m = 0 ∞ a m z m is in H p , 0 < p ≤ 2, of the unit disk of ℂ, then ∑ m = 0 ∞ ( m + 1 ) p - 2 | a m | p ≤ c p ∥ f ∥ p p where c p is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of ℂ n , and use this extension to study some related multiplier problems in ℂ n .

A formula for the Bloch norm of a C 1 -function on the unit ball of ℂ n

Miroslav Pavlović (2008)

Czechoslovak Mathematical Journal

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For a C 1 -function f on the unit ball 𝔹 ⊂ ℂ n we define the Bloch norm by ∥ f ∥ 𝔅 = sup ∥ d ˜ f ∥ , where d ˜ f is the invariant derivative of f , and then show that ∥ f ∥ 𝔅 = sup z , w ∈ 𝔹 z ≠ w ( 1 - | z | 2 ) 1 / 2 ( 1 - | w | 2 ) 1 / 2 | f ( z ) - f ( w ) | | w - P w z - s w Q w z | .

The Bergman projection on weighted spaces: L¹ and Herz spaces

Oscar Blasco, Salvador Pérez-Esteva (2002)

Studia Mathematica

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We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces K p q ( w ) .

The exceptional sets for functions of the Bergman space in the unit ball

Piotr Jakóbczak (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let D be a domain in C 2 . Given w ∈ C , set D w = z ∈ C ∣ z , w ∈ D . If f is a holomorphic and square-integrable function in D , then the set E ⁢ D , f of all w such that f ( ⋅ , w ) is not square-integrable in D w has measure zero. We call this set the exceptional set for f . In this Note we prove that whenever 0 < r < 1 there exists a holomorphic square-integrable function f in the unit ball B in C 2 such that E ⁢ B , f is the circle C ⁢ 0 , r = z ∈ C ∣ z = r .

Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball

Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou (2015)

Annales Polonici Mathematici

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Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator u C φ on H() is defined by u C φ f ( z ) = u ( z ) f ( φ ( z ) ) . We investigate the boundedness and compactness of u C φ induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.