Vol. 302, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Boundedness of singular integrals with flag kernels on weighted flag Hardy spaces

Yongsheng Han, Chin-Cheng Lin and Xinfeng Wu

Vol. 302 (2019), No. 2, 545–598
Abstract

We establish a weighted Hardy space theory associated with flag structures. This theory differs from those in the classical one-parameter and the product settings, and includes weighted Hardy spaces H,wp, weighted Carleson measure spaces CMO,wp (the dual spaces of H,wp), and the boundedness of singular integrals with flag kernels on these spaces. We also derive a Calderón–Zygmund decomposition and provide interpolation of operators acting on H,wp. Examples and counterexamples are constructed to clarify the relations between classes of one-parameter, product and flag Ap weights. The main tool for our approach is the weighted Littlewood–Paley–Stein theory associated with the flag structure.

Keywords
Calderón–Zygmund decomposition, duality, interpolation, singular integrals with flag kernels, weighted flag Carleson measure spaces, weighted flag Hardy spaces
Mathematical Subject Classification 2010
Primary: 42B20
Secondary: 42B30
Milestones
Received: 13 December 2017
Revised: 22 January 2019
Accepted: 27 February 2019
Published: 27 November 2019
Authors
Yongsheng Han
Department of Mathematics
Auburn University
Auburn, AL
United States
Chin-Cheng Lin
National Center for Theoretical Sciences
National Taiwan University
Taipei
Taiwan
Department of Mathematics
National Central University
Chung-Li
Taiwan
Xinfeng Wu
Department of Mathematics
China University of Mining and Technology
Beijing
China