Displaying similar documents to “On some inequalities in holomorphic function theory in polydisk related to diagonal mapping”

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 .

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.

Boundary vs. interior conditions associated with weighted composition operators

Kei Izuchi, Yuko Izuchi, Shûichi Ohno (2014)

Open Mathematics

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Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk 𝔻 , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior 𝔻 and on the boundary ∂ 𝔻 respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators. ...