Abstract
We show that the set defined by digit restrictions contains arbitrarily long arithmetic progressions if and only if its Assouad dimension is one. Moreover, we show that for any $$0\le s\le 1$$ , there exists some set on $$\mathbb {R}$$ with Hausdorff dimension s whose Fourier dimension is zero and it contains arbitrarily long arithmetic progressions.
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
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 call
