Hardy classes and related spaces of analytic functions in the unit circle, polydisc, and the ball

DOI10.1007/BF01087546zbMath0632.32005MaRDI QIDQ1095283

S. V. Shvedenko

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hardy classesintegral representationboundary valuesBMOATaylor coefficientsspaces of analytic functionsharmonic majorants

Mathematics Subject Classification ID

Spaces of bounded analytic functions of one complex variable (30H05) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Boundary behavior of holomorphic functions of several complex variables (32A40) Power series, series of functions of several complex variables (32A05) Other generalizations of function theory of one complex variable (32A30) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Algebras of holomorphic functions of several complex variables (32A38) Global boundary behavior of holomorphic functions of several complex variables (32E35)

Related Items

From integral estimates of functions to uniform ones. II: Sharp versions ⋮ On coefficient multipliers for area Privalov classes ⋮ On the best linear approximation of holomorphic functions ⋮ Approximation of derivatives of analytic functions from one Hardy class by another Hardy class ⋮ Three extremal problems in the Hardy and Bergman spaces of functions analytic in a disk ⋮ Best approximation methods and widths for some classes of functions in \(H_{q,\rho}\), \(1 \leq q\leq\infty\), \(0 < \rho\leq 1\)

Cites Work

• Inequalities of Fejer-Riesz type for holomorphic functions on certain product domains
• Singular integrals on bounded symmetric domains in \(C^ n\).
• Isomorphismes entre espaces \(H_ 1\)
• Hausdorff measure, BMO, and analytic functions
• On the lacunary coefficients of power series
• A contribution to best approximation in the L\(^2\) norm
• The Poisson integral for generalized half-planes and bounded symmetric domains
• On the characteristic of functions meromorphic in the unit disk and of their integrals
• Some remarks on Teichmüller's space of Riemann surfaces
• Bounded Hadamard products of \(H^ p\) functions
• Subordinate \(H^ P\) functions
• Factorization of analytic functions with \(H^ p\) derivative
• Extending bounded holomorphic functions from certain subvarieties of a polydisc
• Coefficient multipliers of \(H^ p\) and \(B^ p\) spaces
• On the boundary behavior of analytic functions without Koebe arcs
• Mean growth and coefficients of \(H^ p\) functions
• Zeros of Lipschitz functions analytic in the unit disc
• An extension of the Hausdorff-Young theorem
• A characterization of zero sets for \(A^ \infty\)
• Remarks on extremum problems in \(H^ 1\)
• \(H^ p\) spaces and conformal mapping
• On the Riesz uniqueness theorem for functions of nearly bounded characteristics
• Interpolation problems in function spaces
• The dual space of \(H^p\) of the polydisc for \(0<p<1\)
• Some uniqueness theorems for \(H^p(U^n)\) functions
• Boundary values and mapping properties of \(H^p\) functions
• Extreme points and unicity of extremum problems in H\(^1\) on polydiscs
• The dual of an inequality of Hardy and Littlewood and some related inequalities
• The containing Fréchet space for the class \(N^+\)
• The failure of interior-exterior factorization in the polydisc and the ball
• Lipschitz spaces of functions on the circle and the disc
• \(H^p\) spaces of several variables
• Zero sets in H\(^p\)(U\(^n\))
• Factorizations of bounded holomorphic functions
• Interpolations by bounded analytic functions and the corona problem
• Some geometric aspects of functions of Hardy class \(H^ p\)
• On the zeros of functions with finite Dirichlet integral and some related function spaces
• Holomorphic functions, of arbitrarily slow growth, without radial limits
• On two problems concerning linear transformations in Hilbert space
• Sets of uniqueness for functions regular in the unit circle
• On the zeros of functions with bounded Dirichlet integrals
• Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann
• Boundary values of analytic functions in several variables and of almost periodic functions
• Nonfactorization Theorems in Weighted Bergman and Hardy Spaces on the Unit Ball of C n (n > 1)
• Bloch Functions in Several Complex Variables, I
• Inequalities for Holomorphic Functions of Several Complex Variables
• Harmonic and Analytic Functions Of Several Variables and The Maximal Theorem Of Hardy and Littlewood
• An Interpolation Problem for Bounded Analytic Functions
• CLASSES OF HOLOMORPHIC FUNCTIONS OF SEVERAL VARIABLES IN CIRCULAR DOMAINS
• On functions of bounded mean oscillation
• Toeplitz Operators on Bounded Symmetric Domains
• Mean Growth and Smoothness of Analytic Functions
• Removable Singularities for H p -Functions
• A Geometric Characterization of N + Domains
• On the Coefficients of Bloch Functions
• Removable Singularities for n-Harmonic Functions and Hardy Classes in Polydiscs
• Radial Limits of n-Subharmonic Functions in the Polydisc
• $L^{p}$-behaviour of the integral means of analytic functions
• Removable Singularity Sets for Analytic Functions Having Modulus with Bounded Laplace Mass
• On the Extension of H p -Functions in Polydiscs
• Support Points of the Unit Ball of H p (1 p ∞)
• On Homogeneous Polynomials on a Complex Ball
• ZEROS OF HOLOMORPHIC FUNCTIONS OF FINITE ORDER AND WEIGHTED ESTIMATES FOR SOLUTIONS OF THE $\bar\partial$-EQUATION
• Criteria for functions to be Bloch
• Bloch functions in several complex variables. II.
• THE INTEGRAL MEANS OF ANALYTIC FUNCTIONS
• Two Multiplier Theorems for H¹(U²)
• Hardy Spaces and Rearrangements
• A Bloch Function in all H p Classes, but not in BMOA
• The Zygmund Condition for Bloch Functions in the Ball in C n
• On BMOA for Riemann Surfaces
• The Dual of H 1
• A Geometric Characterization of Analytic Functions with Bounded Mean Oscillation
• Composition operators and several complex variables
• Isometries of Weighted Bergman Spaces
• Composition Operators Isolated in the Uniform Operator Topology
• Cyclic elements in some spaces of analytic functions
• Lipschitz spaces of holomorphic and pluriharmonic functions on bounded symmetric domains in $C^N$ (N>1)
• On projections in spaces of bounded analytic functions with applications
• The Taylor series and growth of means.
• Boundary Interpolation Sets for Holomorphic Functions Smooth to the Boundary and BMO
• Smoothness of the Boundary Values of Functions Bounded and Holomorphic in the Disk
• Recoverability of Some Classes of Analytic Functions from their Boundary Values
• Holomorphic Functions with Positive Real Part
• The Multiplicative Cousin Problem and a Zero Set for the Nevanlinna Class in the Polydisc
• The space $N_*$ of holomorphic functions on bounded symmetric domains
• Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces HФ and N*.
• Functions of Vanishing Mean Oscillation
• Unusual Topological Properties of the Nevanlinna Class
• A Characterization of F + ∩N
• Bounded Toeplitz Operators on H 1 and Applications of the Duality Between H 1 and the Functions of Bounded Mean Oscillation
• Toeplitz operators related to certain domains in $C^{n}$
• H p -Functions on Strictly Pseudoconvex Domains
• Mean value theorems for harmonic and holomorphic functions on bounded symmetric domains.
• Isometries of H^p Spaces of Bounded Symmetric Domains
• Composition operators on $F^{+}$
• Valeurs au bord pour les solutions de l'opérateur $d^n$, et caractérisation des zéros des fonctions de la classe de Nevanlinna
• Extensions of Hardy spaces and their use in analysis
• The Bloch-Nevanlinna conjecture revisited
• The projective limit of the $H^p$ spaces
• Mean growth and Taylor coefficients of some topological algebras of analytic functions
• On Hardy Classes and the Area Function
• Suites D'Interpolation Pour les Classes de Bergman de la Boule et du Polydisque de Cⁿ
• On Analytic Functions of Bounded Mean Oscillation
• H ^p theory for the poly-disc
• A Necessary and Sufficient Condition for Bloch Functions
• Criteria for Functions to be of Hardy Class H p
• Toeplitz Operators on the Bergman Spaces and in Several Complex Variables
• ON THE UNIFORM BLASCHKE CONDITION AND THE ZERO SETS OF BOUNDED HOLOMORPHIC FUNCTIONS
• Hankel operators, best approximations, and stationary Gaussian processes
• Sur Le Volume Des Zeros Des Fonctions Holomorphes et Bornees dans la Boule de C n
• On the Distribution of Values of Bounded Analytic Functions
• Analytic Toeplitz and Composition Operators
• Two Theorems Related to the Class H^p log⁺ H
• The Isometries of H^p
• The generation of impulse-equivalent pulse trains
• ON THE DERIVATIVE OF A FUNCTION OF BOUNDED CHARACTERISTIC
• Lp Estimates for (Pluri-) Subharmonic Functions.
• Absolute Convergence Factors for H^p Series
• On the Multipliers of H p Spaces
• H^p multipliers and inequalities of Hardy and Littlewood
• Hankel-Schur multipliers and multipliers of the space \(H^ 1\)
• \(H^\infty\) interpolation from a subset of the boundary
• On the rate of growth of the means \(M^ p\) of holomorphic and pluriharmonic functions on the ball
• Integral formulas for the \(\partial\overline\partial\)-equation and zeros of bounded holomorphic functions in the unit ball
• Free interpolation for holomorphic functions regular to the boundary
• Boundary behaviour and normal meromorphic functions
• Families of transformations in the function spaces \(H^p\)
• Extreme points and extremum problems in \(H_1\)
• On limits of sequences of operators
• The Taylor coefficients of inner functions
• Über die BMOA-Norm von log (1-z)
• A construction of inner functions on the unit ball in \(C^ p\)
• Tangential boundary behavior of functions in Dirichlet-type spaces
• On the \(H^ p\) classes of derivatives of functions orthogonal to invariant subspaces
• Duality and multipliers for mixed norm spaces
• Internal-external factorization in Lumer's Hardy spaces
• On a classification of plane domains for BMOA
• The Nevanlinna factorization in certain classes of analytic functions
• A note on the optimal quadrature in \(H^ p\)
• Hardy spaces on the complex ball are isomorphic to Hardy spaces on the disc, \(1\leq p<\infty\)
• On the primarity of \(H^{\infty}\)-spaces
• Some remarks on the free interpolation by bounded and slowly increasing analytic functions
• Fonctions holomorphes bornees et limites tangentielles
• Valeurs au bord des modules de fonctions holomorphes
• Remarks on subspaces of \(H_ p \)when \(0<p<1\)
• Removable singularities for Bloch and BMO functions
• On some approximation properties of real Hardy spaces \((0<p\leq 1)\)
• Canonical Blaschke-type products for the Nevanlinna area class
• Zero sets for functions from \(\Lambda _{\omega}\)
• The bounded, analytic, Dirichlet finite functions and their fibers
• Bounded mean oscillation on the polydisk
• Multipliers of the Dirichlet space
• On a theorem of Hayman concerning the derivative of a function of bounded characteristic
• A geometric condition which implies BMOA
• Inequalities on Bergman spaces
• On the extension of holomorphic functions with growth conditions across analytic subvarieties
• Free interpolation in \(H^\infty\) and in some other classes of functions. II
• Extension de fonctions analytiques avec estimation
• Ideals and factorization in algebras of analytic functions that are smooth up to the boundary
• The n-width of sets of analytic functions
• Weak-* generators for a class of subalgebras of \(l^1\)
• Zeros of \(H^ p\) functions in several complex variables
• Some representing measures for the ball algebra
• Holomorphic functions of bounded mean oscillation and mapping properties of the Szegö projection
• Optimal nodes for interpolation in Hardy spaces
• Cauchy transforms and Beurling-Carleson-Hayman thin sets
• On analytic functions which are in \(H^ p\) for some positive p
• Inner functions and multipliers of Cauchy type integrals
• V. A. Steklov's problem in the theory of orthogonal polynomials
• Inner functions: noninvariant connected components
• Boundary behavior of spaces of analytic functions
• Inner divisors and composition operators
• Fejer-Riesz inequality for holomorphic functions of several complex variables
• Extension dans des classes de Hardy de fonctions holomorphes et estimations de type Mesures de Carleson pour l'équation \(\bar\partial\)
• Holomorphic mappings in the Nevanlinna class
• Hyperbolic Hardy classes and hyperbolically Dirichlet-finite functions
• The non-isomorphism of \(H^1\)-spaces in one and several variables
• Lipschitz spaces of holomorphic functions over bounded symmetric domains in \(C^ n\).
• Interpolation of quasilinear operators and inequalities for entire functions in symmetric spaces
• Interpolation by functions in Bergman spaces
• The zeros of functions in Nevanlinna's area class
• Interpolation, continuation, and quadratic inequalities
• Zeros of functions in the Bergman spaces
• Inner functions under uniform topology
• One-sided maximal functions and H\(^p\)
• Properties of the space \(\widetilde h^p\) (\(0<p\leq 1\)) of harmonic functions on the unit disc
• Some analytic functions whose boundary values have bounded mean oscillation
• The component of the origin in the Nevanlinna class
• Zeros of \(A^p\) functions and related classes of analytic functions
• An extension of the Nevanlinna theory
• Factorization theorems for Hardy spaces in several variables
• An application of the theorem of Rudin to the Toeplitz operators on odd spheres
• On the growth of functions omitting large sets
• Representation of linear functionals in \(H^p\) spaces over bounded symmetric domains in \(\mathbb{C}^N\)
• Analytic functions with bounded mean oscillation and logarithms of \(H^p\) functions
• A note on Lipschitz classes
• Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Berman spaces
• Factorization for non-Nevanlinna classes of analytic functions
• On a class of spaces of analytic functions
• Factorization theorems for functions in the Bergman spaces
• Omitted values of singular inner functions
• BMO functions and the \(\overline\partial\)-equation
• Schlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation
• Inner functions invariant connected components
• Boundary value estimation of the range of an analytic function
• Multiplication by the coordinate functions on the Hardy space of the unit sphere in \(\mathbb{C}^n\)
• Abstract analytic function theory and Hardy algebras
• Toeplitz operators in several complex variables
• Zeros of functions in weighted Bergman spaces
• Semigroups of analytic functions and composition operators
• Good/irreducible inner functions on a polydisc
• A geometric condition for bounded mean oscillation
• Sur la formule de Jensen et les zéros des fonctions holomorphes dans le polydisque
• Holomorphic Lipschitz functions in balls
• Free interpolation in \(H\infty\) and in some other function classes
• Invertible and weakly invertible singular inner functions in the Bergman spaces
• The atomic decomposition for Hardy spaces in several complex variables
• A representation of \(H^ p\)-functions with \(0<p<\infty\)
• On isometries of the Bloch space
• Some properties of fractional integrals. II
• Properties of H p (0 < p < 1) and Its Containing Banach Space
• Two Results Concerning the Zeros of Functions with Finite Dirichlet Integral
• Shorter Notes: Positive H 1/2 Functions are Constants
• Bounded Analytic Functions and Absolutely Continuous Measures
• Zeros of Analytic Functions with Infinitely Differentiable Boundary Values
• H p Spaces on Bounded Symmetric Domains
• The second duals of certain spaces of analytic functions
• Some Results Concerning Multipliers of H ^p
• On Bloch Functions
• On the Generalized Blaschke Condition
• On the Zeros of Functions with Derivatives in H₁ and H_∞
• Boundary values of holomorphic functions
• Isometries of H^p(Uⁿ)
• On the Bloch-Nevanlinna Problem
• On a Class of Functions and Their Integrals
• Multipliers and Linear Functionals for the Class N +
• Mean growth and Taylor coefficients of some classes of functions
• On the Characteristic of Some Classes of Functions and of Their Integrals
• Representation of 𝐻^{𝑝}-functions
• The Modulus of the Boundary Values of Bounded Analytic Functions of Several Variables
• Singular integrals and estimates for the Cauchy-Riemann equations
• On Some Interpolation Problems for Analytic Functions
• Theorems on Fourier Series and Power Series (II)^†
• On the boundary values of functions of several complex variables, I
• Banach spaces of functions analytic in the unit circle, II
• THEOREMS CONCERNING MEAN VALUES OF ANALYTIC OR HARMONIC FUNCTIONS
• [Russian Text Ignored.]
• Denting points in \(B^p\)
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