相关论文: BMOA estimates and radial growth of $B_{\phi}$ fun…
Let $h^\infty_v(\mathbf D)$ and $h^\infty_v(\mathbf B)$ be the spaces of harmonic functions in the unit disk and multi-dimensional unit ball which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling…
In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of $\ell^n_q$-spaces ($1\leq q\leq \infty$) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new…
This announcement considers the following problem. We produce a bounded mean oscillation theorem for small distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$. A revision of this announcement is in the memoir preprint:…
We consider growth conditions for (frequently) Birkhoff-universal functions of exponential type with respect to the different rays emanating from the origin. For that purpose, we investigate their (conjugate) indicator diagram or,…
We study the values of the M\"obius function $\mu$ of intervals in the containment poset of permutations. We construct a sequence of permutations $\pi_n$ of size $2n-2$ for which $\mu(1,\pi_n)$ is given by a polynomial in $n$ of degree 7.…
In this paper, we investigate properties of classes of functions related to certain elliptic operators. Firstly, we prove that a main result of Dyakonov (Acta Math. 178(1997), 143--167) on analytic functions can be extended to this more…
This paper investigates the geometric properties of functions within the generalized Robertson class which consists of alpha-starlike functions of order beta. The study's significance lies in providing a deeper understanding of the…
This article introduces the notion of arithmetic Bohr radius for operator valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. Using tools from local Banach space theory, we determine its asymptotic behavior in…
This article answers the question of V.M. Buchstaber about the growth function of a particular $n$-valued group. This question is closely related to discrete integrable systems. In this paper, we will find a formula for the growth function…
For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha(\mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for…
We investigate properties of ($\alpha,\beta$)-harmonic functions. First, we discuss the coefficient estimates for ($\alpha,\beta$)-harmonic functions. In particular, we obtain Heinz's inequality for ($\alpha,\beta$)-harmonic functions,…
In this article, the new inequalities for the weighted sums of coefficients in the class of bounded functions in the disk are obtained. We develop the methods of I.R.~Kayumov and S.~Ponnusamy, using E.~Reich's theorem on the majorization of…
We consider a bounded radial function f. B. Korenblum and K.E.Zhu give a case where we have equality between the limit near the boundary of the unit disc of the Berezin transform and the limit of the normalized Mellin coefficient when one…
Let ${{\bf x}}=(x_1,\dots,x_d) \in [-1,1]^d$ be linearly independent over $\mathbb Z$, set $K=\{(e^{z},e^{x_1 z},e^{x_2 z}\dots,e^{x_d z}): |z| \le 1\}.$ We prove sharp estimates for the growth of a polynomial of degree $n$, in terms of…
Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the…
We discuss the multipolar expansion of the electromagnetic field with an emphasis on the radiated field. We investigate if the employment of Jefimenko's equations brings a new insight into the calculation of the radiation field. We show…
There are ten chapters in this dissertation, which focuses on nine contents: growth estimates for a class of subharmonic functions in the half plane; growth estimates for a class of subharmonic functions in the half space; a generalization…
We study Bohr type inequalities within the framework of fractional calculus. Using Riemann Liouville fractional differential and integral operators, we establish generalized Bohr radii for analytic functions in the unit disk, including the…
A new proof of the inequalities of D. J. Hallenbeck for the Area functions of multipliers of fractional Cauchy transforms is given.
We consider maximal kernel-operators on abstract measure spaces $(X,\mu)$ equipped with a ball-basis. We prove that under certain asymptotic condition on the kernels those operators maps boundedly BMO(X) into BLO(X), generalizing the…