scholarly journals Multidimensional Hausdorff operators on the real Hardy space

2007 ◽  
Vol 83 (1) ◽  
pp. 79-86 ◽  
Author(s):  
A. K. Lerner ◽  
E. Liflyand
Keyword(s):  
Hardy Space ◽  
The Real ◽  
Real Hardy Space ◽  
Hausdorff Operators ◽  
Wide Family

AbstractFor a wide family of multivariate Hausdorff operators, the boundedness of an operator from this family i s proved on the real Hardy space. By this we extend and strengthen previous results due to Andersen and Móricz.

scholarly journals On a rational approximation problem in the real Hardy space H2

1992 ◽  
Vol 94 (2) ◽  
pp. 175-197 ◽  
Author(s):  
L. Baratchart ◽  
M. Olivi ◽  
F. Wielonsky
Keyword(s):  
Hardy Space ◽  
Rational Approximation ◽  
Approximation Problem ◽  
The Real ◽  
Real Hardy Space

Trigonometric Multipliers on H2π

2005 ◽  
Vol 48 (3) ◽  
pp. 370-381 ◽  
Author(s):  
J. E. Daly ◽  
S. Fridli
Keyword(s):  
Hardy Space ◽  
The Real ◽  
Real Hardy Space

AbstractIn this paper we consider multipliers on the real Hardy space H2π. It is known that the Marcinkiewicz and the Hörmander–Mihlin conditions are sufficient for the corresponding trigonometric multiplier to be bounded on , 1 < p < ∞. We show among others that the Hörmander– Mihlin condition extends to H2π but the Marcinkiewicz condition does not.

On Schauder bases in Hardy spaces

1983 ◽  
Vol 93 (3-4) ◽  
pp. 259-263 ◽  
Author(s):  
P. Oswald
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Schauder Basis ◽  
Dimensional Torus ◽  
Franklin System ◽  
One Dimensional ◽  
The Real ◽  
Real Hardy Space ◽  
Schauder Bases ◽  
The One

SynopsisIt is proved that in the case ½<p<l the periodic Franklin system forms a Schauder basis for the real Hardy space Hp(T) defined on the one-dimensional torus.In this note we prove the followingTheorem. The periodic Franklin system forms a Schauder basis in the real Hardyspace Hp(T) defined on the one-dimensional torus if ½<p< l.

Norm of the Hausdorff Operator on the Real Hardy Space $$H^1({{\mathbb {R}}})$$ H 1 ( R )

2017 ◽  
Vol 12 (1) ◽  
pp. 235-245 ◽  
Author(s):  
Ha Duy Hung ◽  
Luong Dang Ky ◽  
Thai Thuan Quang
Keyword(s):  
Hardy Space ◽  
Hausdorff Operator ◽  
The Real ◽  
Real Hardy Space

scholarly journals Boundedness of Multidimensional Dunkl-Hausdorff Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Radouan Daher ◽  
Faouaz Saadi
Keyword(s):  
Hardy Space ◽  
Sufficient Conditions ◽  
Hausdorff Operator ◽  
Lebesgue Spaces ◽  
Dunkl Operators ◽  
Weighted Lebesgue Spaces ◽  
Hausdorff Operators

In the present paper, we introduce the multidimensional Dunkl-Hausdorff operator ℋκ and we give simple sufficient conditions so that these operators be bounded on the weighted lebesgue spaces Lκpℝn and in the Hardy space Hκ1ℝn associated with the Dunkl operators. We also determine the Dunkl-Hausdorff operator ℋκ∗ that is adjoint to ℋκ.

scholarly journals The Hausdorff operators on the real Hardy spaces Hp(R)

2001 ◽  
Vol 148 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Yuichi Kanjin
Keyword(s):  
Hardy Spaces ◽  
The Real ◽  
Hausdorff Operators
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