The condition of almost everywhere convergence for a functional series with a weak analogue of the orthonormality property

2016 ◽  
Vol 71 (2) ◽  
pp. 61-67
Author(s):  
V. V. Galatenko ◽  
T. P. Lukashenko ◽  
V. A. Sadovnichii
Keyword(s):  
Almost Everywhere Convergence ◽  
Functional Series ◽  
Almost Everywhere ◽  
Weak Analogue

Notes on the Unconditional Convergence of Multidimensional Functional Series

2000 ◽  
Vol 7 (2) ◽  
pp. 215-220
Author(s):  
G. Bareladze
Keyword(s):  
Unconditional Convergence ◽  
Partial Sums ◽  
Almost Everywhere Convergence ◽  
Functional Series ◽  
Almost Everywhere ◽  
Definition Of ◽  
The Way

Abstract The convergence of a multidimensional functional series essentially depends on the way its partial sums are formed. Different ways of definition of partial sums lead to different kinds of convergence. In the paper relations between various kinds of unconditional almost everywhere convergence of multidimensional functional series are studied.

VMO Space Associated with Parabolic Sections and its Application

2015 ◽  
Vol 58 (3) ◽  
pp. 507-518
Author(s):  
Ming-Hsiu Hsu ◽  
Ming-Yi Lee
Keyword(s):  
Hardy Space ◽  
Weak Convergence ◽  
Bounded Sequence ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere

AbstractIn this paper we define a space VMO𝒫 associated with a family 𝒫 of parabolic sections and show that the dual of VMO𝒫 is the Hardy space . As an application, we prove that almost everywhere convergence of a bounded sequence in implies weak* convergence

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