Lacunary Series in Qk Spaces
نویسندگان
چکیده
Under mild conditions on the weight function K we characterize lacunary series in the so-called QK spaces.
منابع مشابه
A note on lacunary series in $mathcal{Q}_K$ spaces
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
متن کاملLacunary Convergence of Series in L0 Lech Drewnowski and Iwo Labuda
For a finite measure λ, let L0(λ) denote the space of λ-measurable functions equipped with the topology of convergence in measure. We prove that a series in L0(λ) is subseries (or unconditionally) convergent provided each of its lacunary subseries converges. A series in a topological vector space is said to be subseries convergent if each of its subseries converges. As is well known, a subserie...
متن کاملLacunary Series in Mixed Norm Spaces on the Ball and the Polydisk
We characterize lacunary series in mixed norm spaces on the unit ball B in C and on the unit polydisk D in C. Introduction and main results Let n be a positive integer. Two domains will be used in the paper: the open unit ball B in C, B = {z ∈ C : |z| < 1 }, and the open unit polydisk D in C, D = {z = (z1, ..., zn) ∈ C : |z1| < 1, ..., |zn| < 1 }. We write D = B = D. Denote by T the Shilov boun...
متن کاملLacunary generalized difference statistical convergence in random 2-normed spaces
Recently in [22], Mursaleen introduced the concept of statistical convergence in random 2-normed spaces. In this paper, we define and study the notion of lacunary ∆-statistical convergence and lacunary ∆-statistical Cauchy sequences in random 2-normed spaces using lacunary density and prove some interesting theorems. Subjclass [2000] : Primary 40A05; Secondary 46A70, 40A99, 46A99.
متن کاملLacunary Ideal Convergence in Probabilistic Normed Space
Abstract. The aim of this paper is to study the notion of lacunary I-convergence in probabilistic normed spaces as a variant of the notion of ideal convergence. Also lacunary I-limit points and lacunary I-cluster points have been defined and the relation between them has been established. Furthermore, lacunary Cauchy and lacunary I-Cauchy sequences are introduced and studied. Finally, we provid...
متن کامل