ABSTRACT
Chapter 5
MODIFIEDH-TRANSFORMS ON THE SPACE L
;r
5.1. Modied H-Transforms
The present chapter is devoted to studying the following modications of the H-transform
(3.1.1):
H
f
(x) =
Z
H
m;n
p;q
"
x
t
(a
i
;
i
)
1;p
(b
j
;
j
)
1;q
#
f(t)
dt
t
; (5.1.1)
H
f
(x) =
Z
H
m;n
p;q
"
t
x
(a
i
;
i
)
1;p
(b
j
;
j
)
1;q
#
f(t)
dt
x
; (5.1.2)
H
;
f
(x) = x
Z
H
m;n
p;q
"
xt
(a
i
;
i
)
1;p
(b
j
;
j
)
1;q
#
t
f(t)dt; (5.1.3)
H
;
f
(x) = x
Z
H
m;n
p;q
"
x
t
(a
i
;
i
)
1;p
(b
j
;
j
)
1;q
#
t
f(t)
dt
t
; (5.1.4)
H
;
f
(x) = x
Z
H
m;n
p;q
"
t
x
(a
i
;
i
)
1;p
(b
j
;
j
)
1;q
#
t
f(t)
dt
x
; (5.1.5)
where ; 2 C .
