Generalized Hausdorff Operators on
K
̇
α
,
q
β
,
p
ℝ
and
H
K
̇
α
,
q
β
,
p
,
N
ℝ
in the Dunkl Settings
Keyword(s):
In the present paper, we obtain some new results, and we generalize some known results for the Hausdorff operators. We have studied the generalized Hausdorff operators H α , φ on the Dunkl-type homogeneous weighted Herz spaces K ̇ α , q β , p ℝ and Dunkl Herz-type Hardy spaces H K ̇ α , q β , p , N ℝ . We have determined simple sufficient conditions for these operators to be bounded on these spaces. As applications, we provide necessary and sufficient conditions for generalized Cesàro operator to be bounded on K ̇ α , q β , p ℝ and Hardy inequality for K ̇ α , q β , p ℝ .
2009 ◽
Vol 7
(3)
◽
pp. 209-223
◽
Keyword(s):
1986 ◽
Vol 23
(04)
◽
pp. 851-858
◽
1991 ◽
Vol 11
(1)
◽
pp. 65-71
◽