An integral operator on analytic functions with negative coefficients.
An integral operator on the classes S*(α) and CVH(β)
The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class CVH(β) and also we estimate the first two coefficients for functions obtained by this operator applied on the class CVH(β).
An integral operator that maps a subclass of starlike functions into itself
An integral related to the Cauchy transform on the Sierpiński gasket.
An integral univalent operator.
An integral univalent operator. II.
An integral univalent operator of the class and .
An interesting lemma for regular -fractions.
An invariant subspace of the Bergman space having the codimension two property.
An inverse approximation theorem on subsets of elliptic curves.
An inverse Sobolev lemma.
We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of Rn to the full range 0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of Rn in terms of the growth of the mapping.
An invitation to the study of univalent and multivalent functions.
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
An isoperimetric inequality for logarithmic capacity.
An observation on the Turán-Nazarov inequality
The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω ≥ μ, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán-Nazarov inequality, they necessarily enter the definition of ω.
An operator preserving inequalities between polynomials.
An ordinary differential operator and its applications to certain classes of multivalently meromorphic functions.
An ultrametric Nevanlinna’s second main theorem for small functions of a special type
In ultrametric Nevanlinna theory, the Nevanlinna’s second main theorem for small functions has only been proved in the case of at most three small functions. In this paper, we prove a second main theorem for small functions of a special type when the residue characteristic of the field is zero.
An univalence criteria for a class of integral operators.
An univalence criterion and the Schwarzian derivative.