scholarly journals Riesz means of Fourier series and integrals: Strong summability at the critical index

2019 ◽  
Vol 372 (4) ◽  
pp. 2959-2999
Author(s):  
Jongchon Kim ◽  
Andreas Seeger
Keyword(s):  
Fourier Series ◽  
Critical Index ◽  
Strong Summability ◽  
Riesz Means

BOCHNER–RIESZ MEANS ON BLOCK-SOBOLEV SPACES IN COMPACT LIE GROUP

2020 ◽  
Vol 109 (2) ◽  
pp. 176-192
Author(s):  
JIECHENG CHEN ◽  
DASHAN FAN ◽  
FAYOU ZHAO
Keyword(s):  
Fourier Series ◽  
Sobolev Space ◽  
Convergence Rate ◽  
Lie Group ◽  
Sobolev Spaces ◽  
Critical Index ◽  
Compact Lie Group ◽  
Riesz Means ◽  
Riesz Mean

On a compact Lie group $G$ of dimension $n$, we study the Bochner–Riesz mean $S_{R}^{\unicode[STIX]{x1D6FC}}(f)$ of the Fourier series for a function $f$. At the critical index $\unicode[STIX]{x1D6FC}=(n-1)/2$, we obtain the convergence rate for $S_{R}^{(n-1)/2}(f)$ when $f$ is a function in the block-Sobolev space. The main theorems extend some known results on the $m$-torus $\mathbb{T}^{m}$.

scholarly journals Weighted Estimates for Bilinear Bochner-Riesz Means at the Critical Index

2020 ◽  
Author(s):  
K. Jotsaroop ◽  
Saurabh Shrivastava ◽  
Kalachand Shuin
Keyword(s):  
Critical Index ◽  
Riesz Means ◽  
Weighted Estimates

scholarly journals The strong summability of Fourier series

1935 ◽  
Vol 25 ◽  
pp. 162-189 ◽  
Author(s):  
G. Hardy ◽  
J. Littlewood
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Summability Of Fourier Series

scholarly journals Absolute and strong summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series and $r$ times differentiated conjugate Fourier series by matrix methods

2021 ◽  
pp. 74
Author(s):  
N.T. Polovina
Keyword(s):  
Fourier Series ◽  
Strong Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series ◽  
The Matrix

We establish conditions of $|\gamma|_p$- and $[\gamma]_p$-summability in degree $p \geqslant 1$ of $r$ times differentiated Fourier series at the point where $\gamma = \| \gamma_{nk} \|$ is the matrix of transformation of series to sequence. Analogous conditions are considered also for $r$ times differentiated conjugate Fourier series.

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