Displaying similar documents to “Norm and Taylor coefficients estimates of holomorphic functions in balls”

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.

On some inequalities in holomorphic function theory in polydisk related to diagonal mapping

Romi F. Shamoyan, Olivera R. Mihić (2010)

Czechoslovak Mathematical Journal

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We present a description of the diagonal of several spaces in the polydisk. We also generalize some previously known contentions and obtain some new assertions on the diagonal map using maximal functions and vector valued embedding theorems, and integral representations based on finite Blaschke products. All our results were previously known in the unit disk.

On holomorphic continuation of functions along boundary sections

S. A. Imomkulov, J. U. Khujamov (2005)

Mathematica Bohemica

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Let D ' ⊂ ℂ n - 1 be a bounded domain of Lyapunov and f ( z ' , z n ) a holomorphic function in the cylinder D = D ' × U n and continuous on D ¯ . If for each fixed a ' in some set E ⊂ ∂ D ' , with positive Lebesgue measure mes E > 0 , the function f ( a ' , z n ) of z n can be continued to a function holomorphic on the whole plane with the exception of some finite number (polar set) of singularities, then f ( z ' , z n ) can be holomorphically continued to ( D ' × ℂ ) ∖ S , where S is some analytic (closed pluripolar) subset of D ' × ℂ .

Holomorphic Sobolev spaces on the ball

Frank Beatrous, Jacob Burbea

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CONTENTSIntroduction ..............................................................50. Preliminaries and notation....................................61. Hilbert spaces of holomorphic functions..............112. Some estimates ..................................................163. The space L q p ............................................224. Norm estimates...................................................305. Sobolev norms....................................................356. Projections...

Boundary functions on a bounded balanced domain

Piotr Kot (2009)

Czechoslovak Mathematical Journal

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We solve the following Dirichlet problem on the bounded balanced domain Ω with some additional properties: For p > 0 and a positive lower semi-continuous function u on ∂ Ω with u ( z ) = u ( λ z ) for | λ | = 1 , z ∈ ∂ Ω we construct a holomorphic function f ∈ 𝕆 ( Ω ) such that u ( z ) = ∫ 𝔻 z | f | p d 𝔏 𝔻 z 2 for z ∈ ∂ Ω , where 𝔻 = { λ ∈ ℂ | λ | < 1 } .

On a class of ∂ ¯ -equations without solutions

Telemachos Hatziafratis (1998)

Commentationes Mathematicae Universitatis Carolinae

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In this note we construct ∂ ¯ -equations (inhomogeneous Cauchy-Riemann equations) without solutions. The construction involves Bochner-Martinelli type kernels and differentiation with respect to certain parameters in appropriate directions.