General Fourier coefficients and almost everywhere convergence

2021 ◽  
Vol 85 (2) ◽  
Author(s):  
Larry Davidovich Gogoladze ◽  
Giorgi Cagareishvili
Keyword(s):  
Fourier Coefficients ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere

On the almost everywhere convergence of Fourier series

1967 ◽  
Vol 63 (3) ◽  
pp. 703-705 ◽  
Author(s):  
B. S. Yadav
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
Modulus Of Continuity ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Modulus Of Smoothness ◽  
General Concept ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Image Position

Let f be a 2π-periodic function of the class L(−π,π). PutWe call, with Žuk(6), the quantity L(p)(h, f) the L-modulus of smoothness of order p of the function f. Žuk has recently obtained, in (5) and (6), generalizations of a number of classical results on the absolute convergence of Fourier series, as also on the order of Fourier coefficients by employing the concept of the L-modulus of smoothness which is obviously a more general concept than that of the modulus of continuity. It is the purpose of this note to prove a theorem on the almost everywhere convergence of Fourier series of f involving the concept of L(p)(h, f).

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

scholarly journals Restriction of Families of Conversion Operators in Lp Spaces

2021 ◽  
Vol 27 (3) ◽  
pp. 449-460
Author(s):  
A. D. Nakhman
Keyword(s):  
Fourier Coefficients ◽  
Continuous Functions ◽  
Parameter Family ◽  
Maximal Operators ◽  
Limiting Behavior ◽  
Lp Spaces ◽  
Almost Everywhere ◽  
Spaces Of Continuous Functions

We study a one-parameter family of convolutional operators acting in Lebesgue Lp spaces. The case of integral kernels given by the Fourier coefficients is considered. It is established that the condition of the coefficients being quasiconvex ensures the boundedness of the corresponding maximal operators. The limiting behavior of families in the metrics of spaces of continuous functions and Lp, p ≥ 1, classes is studied, and their convergence is obtained almost everywhere. The ways of possible generalizations and distributions are indicated.

Sign in / Sign up

Export Citation Format

Share Document