Extension and integral representation of the finite Hilbert transform in rearrangement invariant spaces

2019 ◽  
Vol 43 (5-6) ◽  
pp. 783-812 ◽  
Author(s):  
Guillermo P. Curbera ◽  
Susumu Okada ◽  
Werner J. Ricker
Keyword(s):  
Integral Representation ◽  
Hilbert Transform ◽  
Rearrangement Invariant Spaces ◽  
Finite Hilbert Transform ◽  
Invariant Spaces

The Hilbert Transform on Rearrangement-Invariant Spaces

1967 ◽  
Vol 19 ◽  
pp. 599-616 ◽  
Author(s):  
D. W. Boyd
Keyword(s):  
Linear Operator ◽  
Function Space ◽  
Hilbert Transform ◽  
Bounded Linear Operator ◽  
Lorentz Spaces ◽  
Bounded Linear ◽  
Rearrangement Invariant Spaces ◽  
The Hilbert Transform ◽  
Invariant Spaces

The purpose of this paper is to investigate conditions under which the Hilbert transform defines a bounded linear operator from a given function space into itself. The spaces with which we deal have the property of rearrangement-invariance which is defined in §1. This class of spaces includes the Lebesgue, Orlicz, and Lorentz spaces.

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
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