Inequalities for the finite Hilbert transform of functions with bounded divided differences

2020 ◽  
Vol 29 (1) ◽  
pp. 17-26
Author(s):  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Hilbert Transform ◽  
Divided Differences ◽  
Finite Hilbert Transform ◽  
Complex Valued

In this paper we establish some inequalities for the finite Hilbert transform of complex valued functions for which the divided differences in any two points of the interval are bounded. Applications for some particular functions of interest are provided as well.

scholarly journals Approximating the finite Hilbert transform via trapezoid type inequalities

2002 ◽  
Vol 43 (10-11) ◽  
pp. 1359-1369 ◽  
Author(s):  
N.M. Dragomir ◽  
S.S. Dragomir ◽  
P. Farrell
Keyword(s):  
Hilbert Transform ◽  
Finite Hilbert Transform

A UNIFORM INEQUALITY FOR THE FINITE HILBERT TRANSFORM IN WEIGHTED LEBESQUE SPACES

1988 ◽  
Vol 21 (2) ◽  
pp. 529-538
Author(s):  
Elias Wegert ◽  
Lothar ν. Wolfersdorf
Keyword(s):  
Hilbert Transform ◽  
Finite Hilbert Transform

scholarly journals Inversion and extension of the finite Hilbert transform on $$\mathbf {(-1,1)}$$

2019 ◽  
Vol 198 (5) ◽  
pp. 1835-1860 ◽  
Author(s):  
Guillermo P. Curbera ◽  
Susumu Okada ◽  
Werner J. Ricker
Keyword(s):  
Hilbert Transform ◽  
Finite Hilbert Transform
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