scholarly journals Almost everywhere summability of multiple Walsh–Fourier series

2003 ◽  
Vol 287 (1) ◽  
pp. 90-100 ◽  
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Almost Everywhere ◽  
Almost Everywhere Summability

scholarly journals Maximal transference and summability of multilinear Fourier series

2006 ◽  
Vol 80 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Loukas Grafakos ◽  
Petr Honzík
Keyword(s):  
Fourier Series ◽  
Multilinear Operators ◽  
Almost Everywhere Convergence ◽  
Almost Everywhere ◽  
Transference Theorem ◽  
Almost Everywhere Summability

AbstractWe obtain a maximal transference theorem that relates almost everywhere convergence of multilinear Fourier series to boundedness of maximal multilinear operators. We use this and other recent results on transference and multilinear operators to deduce Lp and almost everywhere summability of certain m–linear Fourier series. We formulate conditions for the convergence of multilinear series and we investigate certain kinds of summation.

scholarly journals Generalized localization for spherical partial sums of multiple Fourier series

2019 ◽  
Vol 489 (1) ◽  
pp. 7-10
Author(s):  
R. R. Ashurov
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series ◽  
Partial Sums ◽  
Localization Principle ◽  
Open Set ◽  
Almost Everywhere

In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L2-class is proved, that is, if f L2 (ТN) and f = 0 on an open set ТN then it is shown that the spherical partial sums of this function converge to zero almost - ​everywhere on . It has been previously known that the generalized localization is not valid in Lp (TN) when 1 p 2. Thus the problem of generalized localization for the spherical partial sums is completely solved in Lp (TN), p 1: if p 2 then we have the generalized localization and if p 2, then the generalized localization fails.

Sign in / Sign up

Export Citation Format

Share Document