Rearrangement inequality for periodic functions

1976 ◽  
Vol 61 (1) ◽  
pp. 35-44 ◽  
Author(s):  
R. Friedberg ◽  
J. M. Luttinger
Keyword(s):  
Periodic Functions ◽  
Rearrangement Inequality

On finite sums of periodic functions

2020 ◽  
Vol 27 (2) ◽  
pp. 265-269
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Analytic Function ◽  
Real Line ◽  
Real Analytic Function ◽  
Periodic Functions ◽  
Uniform Limit ◽  
The Real ◽  
Pointwise Limit ◽  
Finite Sums ◽  
Real Analytic

AbstractIt is shown that any function acting from the real line {\mathbb{R}} into itself can be expressed as a pointwise limit of finite sums of periodic functions. At the same time, the real analytic function {x\rightarrow\exp(x^{2})} cannot be represented as a uniform limit of finite sums of periodic functions and, simultaneously, this function is a locally uniform limit of finite sums of periodic functions. The latter fact needs the techniques of Hamel bases.

The Rearrangement Inequality for the Ergodic Maximal Function

2001 ◽  
Vol 8 (4) ◽  
pp. 727-732
Author(s):  
L. Ephremidze
Keyword(s):  
Maximal Function ◽  
Rearrangement Inequality ◽  
Decreasing Rearrangement ◽  
Exact Constants

Abstract The equivalence of the decreasing rearrangement of the ergodic maximal function and the maximal function of the decreasing rearrangement is proved. Exact constants are obtained in the corresponding inequalities.

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