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Vol 54, No 3 (2019)
- Year: 2019
- Articles: 6
- URL: https://journals.rcsi.science/1068-3623/issue/view/14100
Functional Analysis
Essential Norm of Weighted Composition Operators from Analytic Besov Spaces into Zygmund Type Spaces
Abstract
In this paper, we give some estimates for the essential norm of weighted composition operators from analytic Besov spaces into Zygmund type spaces. In particular, a new characterization for the boundedness and compactness of the weighted composition operators uCϕ is obtained.
129-142
On Excess of Retro Banach Frames
Abstract
The excess of a frame is the greatest number of elements that can be removed from a given frame, yet leave a set which is a frame for the underlying space. We present a characterization of retro Banach frames in Banach spaces with finite excess. A sufficient condition for the existence of a retro Banach frame with infinite excess is obtained.
143-146
Real and Complex Analysis
Uniform Convergence of Double Vilenkin-Fourier Series
Abstract
In this paper we study the problem of uniform convergence for the rectangular partial sums of double Fourier series on a bounded Vilenkin group of functions of partial bounded oscillation.
147-156
Meromorphic Functions Sharing Three Values with Their Linear Differential Polynomials in an Angular Domain
Abstract
Let f be a nonconstant meromorphic function of lower order µ (f) > 1/2 in ℂ, and let aj (j = 1, 2, 3) be three distinct finite complex numbers. We show that there exists an angular domain D = {z: α ≤ arg z ≤ β}, where 0 < β − α ≤ 2π, such that if f share aj (j = 1, 2, 3) CM with its k-th linear differential polynomial L[f] in D, then f = L[f]. This generalizes the corresponding results from Frank and Schwick, Zheng and Li-Liu-Yi.
157-162
On the Structure of Functions, Universal for Weighted Spaces \(L_\mu ^p\left[ {0,1} \right],p > 1\)
Abstract
The paper is devoted to the questions relating the structure of universal functions for weighted spaces \(L_\mu ^p\left[{0,\;1} \right],\;p > 1\). We prove existence of a measurable set E ⊂ [0, 1] with measure arbitrarily close to 1, and a weight function 0 < µ(x) ≤ 1, equal to 1 on E, such that by suitable continuation of an arbitrary function f ∈ L1(E) on [0, 1] \ E, a function \(\widetilde{f}\; \in \;{L^1}\left[{0,\;1} \right]\) can be obtained, which is universal for each class \(L_\mu ^p\left[{0,\;1} \right],\;p > 1\), in the sense of subsequences of signs of its Fourier-Walsh coefficients.
163-175
On an Open Problem of Zhang and Xu
Abstract
Taking an open problem in [25] into background we employ the idea of normal family to investigate the uniqueness problem of meromorphic functions sharing a non-zero polynomial which improves a number of existing results. Specially we rectify some errors and gaps in a recent result of P. Sahoo [15].
176-190