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Zeitschrift für Analysis und ihre Anwendungen


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Volume 39, Issue 4, 2020, pp. 433–460
DOI: 10.4171/ZAA/1667

Published online: 2020-10-22

Vector Valued Maximal Carleson Type Operators on the Weighted Lorentz Spaces

Dao Van Duong[1], Kieu Huu Dung[2] and Nguyen Minh Chuong[3]

(1) Mientrung University of Civil Engineering, Phu Yen, Vietnam
(2) University of Transport and Communications, Hanoi, Vietnam
(3) Vietnamese Academy of Science and Technology, Hanoi, Vietnam

In this paper, by using the idea of linearizing maximal operators originated by Charles Fefferman and the $TT*$ method of Stein–Wainger, we establish a weighted inequality for vector valued maximal Carleson type operators with singular kernels proposed by Andersen and John on the weighted Lorentz spaces with vector-valued functions.

Keywords: Vector-valued Carleson operator, maximal function, singular integral, $A_p$-weight, Lorentz space

Duong Dao Van, Dung Kieu Huu, Chuong Nguyen Minh: Vector Valued Maximal Carleson Type Operators on the Weighted Lorentz Spaces. Z. Anal. Anwend. 39 (2020), 433-460. doi: 10.4171/ZAA/1667