TY - JOUR
T1 - Hausdorff operators associated with the Opdam–Cherednik transform in Lebesgue spaces
AU - Mondal, Shyam Swarup
AU - Poria, Anirudha
N1 - Funding Information:
The first author gratefully acknowledges the support provided by IIT Guwahati, Government of India. The second author is deeply indebted to Prof. Nir Lev for several fruitful discussions and generous comments. The authors wish to thank the anonymous referee for valuable comments and suggestions that helped to improve the quality of the paper.
Funding Information:
Research supported by ERC Starting Grant No. 713927.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/9
Y1 - 2022/9
N2 - In this paper, we introduce the Hausdorff operator associated with the Opdam–Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam–Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.
AB - In this paper, we introduce the Hausdorff operator associated with the Opdam–Cherednik transform and study the boundedness of this operator in various Lebesgue spaces. In particular, we prove the boundedness of the Hausdorff operator in Lebesgue spaces, in grand Lebesgue spaces, and in quasi-Banach spaces that are associated with the Opdam–Cherednik transform. Also, we give necessary and sufficient conditions for the boundedness of the Hausdorff operator in these spaces.
KW - Grand Lebesgue spaces
KW - Hausdorff operator
KW - Lebesgue spaces
KW - Opdam–Cherednik transform
KW - Quasi-Banach spaces
UR - http://www.scopus.com/inward/record.url?scp=85130992726&partnerID=8YFLogxK
U2 - 10.1007/s11868-022-00462-x
DO - 10.1007/s11868-022-00462-x
M3 - Article
AN - SCOPUS:85130992726
SN - 1662-9981
VL - 13
JO - Journal of Pseudo-Differential Operators and Applications
JF - Journal of Pseudo-Differential Operators and Applications
IS - 3
M1 - 31
ER -