Weighted Hardy and Cesàro operators on Heisenberg group and their norms

ABSTRACT

For weighted Hardy and Cesàro operators on Heisenberg group ${\mathbb{H}}^n$, we give the exact values for its norms in Morrey space, its central variant and $BLO\left({\mathbb{H}}^n\right)$. Also we prove the sharp two-sided estimate for its norm in Herz space. These statements are analogues of results due to Z.W.Fu and S.Z.Lu (Morrey and Herz spaces), S.S.Volosivets (BLO space) and generalize previous result concerning $L^q\left({\mathbb{H}}^n\right)$ space by Chu et al.

KEYWORDS:

• Weighted Hardy operator
• weighted Cesàro operator
• Heisenberg group
• Morrey space
• Herz space
• BLO space

AMS SUBJECT CLASSIFICATION:

• 43A15
• 43A80
• 26D15
• 22E25

Acknowledgements

The author thanks both referees for their valuable suggestions to improve the text of paper.

Disclosure statement

No potential conflict of interest was reported by the authors.