Abstract
Markov's inequality for the maxima of the derivatives of polynomials over cubes is replaced by an inequality where the cubes are changed to certain cubes intersected by a given subset F of R n . This new inequality is true for certain sets F and false for others. We are interested in the sets F for which this inequality is true and we prove that these sets must have positive Hausdorff dimension. Our inequality is not true if F is the closure of a domain with an outgoing cusp. We introduce a generalized inequality which holds for these sets and prove that this new inequality allows sets F with Hausdorff dimension zero.
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.
