Thickness conditions and Littlewood–Paley sets
Volume 220 / 2014
                    
                    
                        Studia Mathematica 220 (2014), 265-276                    
                                        
                        MSC: Primary 42A45; Secondary 43A46.                    
                                        
                        DOI: 10.4064/sm220-3-4                    
                                    
                                                Abstract
We consider sets in the real line that have Littlewood–Paley properties $\mathrm {LP}(p)$ or $\mathrm {LP}$ and study the following question: How thick can these sets be?
 
             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                         
                                                            