Spaces of piecewise-continuous almost-periodic functions and almost-periodic sets on the real line. II

1992 ◽  
Vol 44 (3) ◽  
pp. 338-347 ◽  
Author(s):  
A. M. Samoilenko ◽  
S. I. Trofimchuk
Keyword(s):  
Real Line ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
The Real ◽  
Periodic Sets ◽  
Piecewise Continuous

scholarly journals On extensions of inequalities of Kolmogoroff and others and some applications to almost periodic functions

1972 ◽  
Vol 13 (1) ◽  
pp. 1-16 ◽  
Author(s):  
C. J. F. Upton
Keyword(s):  
Real Function ◽  
Real Line ◽  
Complex Function ◽  
Real Variable ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Everywhere ◽  
Image Position

Let f(x) be a complex function of a real variable, defined over the whole real line, which possesses n derivatives (the nth at least almost everywhere) and is such that . Then, if k is any integer for which 0< k < n, Kolmogoroff's inequality may be written as,or, by putting ,The constant K=K (k, n) known explicitly and is the best possible, i.e., there is a (real) function for which equality holds (see Bang [1]).

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