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Papers by Janusz Godula

Research paper thumbnail of On regularity theorems for linearly invariant families of analytic functions in the unit polydisk

Research paper thumbnail of Generalized hankel operators on the bergman space on the unit ball

Complex Variables and Elliptic Equations, 1997

ABSTRACT

Research paper thumbnail of Meromorphic univalent functions in an annulus

Rendiconti del Circolo Matematico di Palermo, 1987

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Se..fi9 II, Tcrno XXXVI (1987), pp. 474-484 ... We c... more RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Se..fi9 II, Tcrno XXXVI (1987), pp. 474-484 ... We consider the integral means for the class of functions which are meromorphic and univalent in an annulus. ... Let lo be fixed with p > 1. Let F(p) denote the class of all ...

Research paper thumbnail of On a class of functions defined on a ring

Research paper thumbnail of On One Property of Functions with Positive Real Part in a Ring

Research paper thumbnail of Linearly invariant families of holomorphic functions in the unit polydisc

Banach Center Publications

In this paper we extend the definition of the linearly invariant family and the definition of the... more In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.

Research paper thumbnail of Order of linearly invariant family of mappings in

In this paper we suggest a new definition of the order of a linearly invariant family of locally ... more In this paper we suggest a new definition of the order of a linearly invariant family of locally biholomorphic mappings of the unit ball in . This definition is equivalent to the one given by Pfaltzgraff in [J.A. PfaltzgraffComplex Variables Theory Appl33 (1997), 239–253.]. It bases on a very simple relationship with the Jacobian of the mappings (see Corollary 1). It appears that the order of a mapping depends only on its Jacobian (see Proposition 1).

Research paper thumbnail of Linearly invariant families, Bloch functions and uniformly perfect sets

Complex Variables and Elliptic Equations, 2011

ABSTRACT

Research paper thumbnail of On Regularity Theorems for Linearly Invariant Families of Harmonic Functions

Issues of Analysis, 2015

The classical theorem of growth regularity in the class S of analytic and univalent in the unit d... more The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions f describes the growth character of different functionals of f ∈ S and z ∈ ∆ as z tends to ∂∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sensepreserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.

Research paper thumbnail of Integral means of holomorphic functions in the unit ball

Research paper thumbnail of On some classes of regular univalent functions

Research paper thumbnail of On the property of functions with positive real part in a ring

Research paper thumbnail of Integral means of derivatives of functions on the unit ball

Research paper thumbnail of Some remarks on Bazilevič functions

Research paper thumbnail of On Bloch functions and univalence of the integral of (h ' ) λ

Research paper thumbnail of Integral means of univalent functions with Montels’s normalization

Research paper thumbnail of On a class of Bazilevic functions

Research paper thumbnail of On univalence of a certain integral

Research paper thumbnail of G p (α)-norm of the convolution of functions

Research paper thumbnail of On functions angularly accessible in the direction of the imaginary axis

Research paper thumbnail of On regularity theorems for linearly invariant families of analytic functions in the unit polydisk

Research paper thumbnail of Generalized hankel operators on the bergman space on the unit ball

Complex Variables and Elliptic Equations, 1997

ABSTRACT

Research paper thumbnail of Meromorphic univalent functions in an annulus

Rendiconti del Circolo Matematico di Palermo, 1987

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Se..fi9 II, Tcrno XXXVI (1987), pp. 474-484 ... We c... more RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Se..fi9 II, Tcrno XXXVI (1987), pp. 474-484 ... We consider the integral means for the class of functions which are meromorphic and univalent in an annulus. ... Let lo be fixed with p > 1. Let F(p) denote the class of all ...

Research paper thumbnail of On a class of functions defined on a ring

Research paper thumbnail of On One Property of Functions with Positive Real Part in a Ring

Research paper thumbnail of Linearly invariant families of holomorphic functions in the unit polydisc

Banach Center Publications

In this paper we extend the definition of the linearly invariant family and the definition of the... more In this paper we extend the definition of the linearly invariant family and the definition of the universal linearly invariant family to higher dimensional case. We characterize these classes and give some of their properties. We also give a relationship of these families with the Bloch space.

Research paper thumbnail of Order of linearly invariant family of mappings in

In this paper we suggest a new definition of the order of a linearly invariant family of locally ... more In this paper we suggest a new definition of the order of a linearly invariant family of locally biholomorphic mappings of the unit ball in . This definition is equivalent to the one given by Pfaltzgraff in [J.A. PfaltzgraffComplex Variables Theory Appl33 (1997), 239–253.]. It bases on a very simple relationship with the Jacobian of the mappings (see Corollary 1). It appears that the order of a mapping depends only on its Jacobian (see Proposition 1).

Research paper thumbnail of Linearly invariant families, Bloch functions and uniformly perfect sets

Complex Variables and Elliptic Equations, 2011

ABSTRACT

Research paper thumbnail of On Regularity Theorems for Linearly Invariant Families of Harmonic Functions

Issues of Analysis, 2015

The classical theorem of growth regularity in the class S of analytic and univalent in the unit d... more The classical theorem of growth regularity in the class S of analytic and univalent in the unit disc ∆ functions f describes the growth character of different functionals of f ∈ S and z ∈ ∆ as z tends to ∂∆. Earlier the authors proved the theorems of growth and decrease regularity for harmonic and sensepreserving in ∆ functions which generalized the classical result for the class S. In the presented paper we establish new properties of harmonic sense-preserving functions, connected with the regularity theorems. The effects both common for analytic and harmonic case and specific for harmonic functions are displayed.

Research paper thumbnail of Integral means of holomorphic functions in the unit ball

Research paper thumbnail of On some classes of regular univalent functions

Research paper thumbnail of On the property of functions with positive real part in a ring

Research paper thumbnail of Integral means of derivatives of functions on the unit ball

Research paper thumbnail of Some remarks on Bazilevič functions

Research paper thumbnail of On Bloch functions and univalence of the integral of (h ' ) λ

Research paper thumbnail of Integral means of univalent functions with Montels’s normalization

Research paper thumbnail of On a class of Bazilevic functions

Research paper thumbnail of On univalence of a certain integral

Research paper thumbnail of G p (α)-norm of the convolution of functions

Research paper thumbnail of On functions angularly accessible in the direction of the imaginary axis

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