Abstract
W. Kleiner established (1964, Ann. Polon. Math. 14 , 117–130) for smooth curves and arcs an estimate for the discrepancy of a signed measure by using its energy norm. We extend this result to quasiconformal curves and arcs. The proof uses the theory of quasiconformal mappings and condenser theory. In a first step, the discrepancy of a signed measure can be estimated from above in terms of its energy norm and the capacity of a special condenser. This result is valid on every Jordan curve. Examples show the sharpness of the results from various points of view.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
