In this paper, we study the quasi-Beurling dimensions of the spectra for a class of planar Moran measures μ { M k } , D and obtain the exact upper and lower bounds of the quasi-Beurling dimensions under some conditions. Moreover, we prove an intermediate value property, i.e., for any t ∈ [ 0 , dim ‾ e μ { M k } , D ] , there exists a spectrum Λ t of μ such that dim q B Λ t = t , where dim ‾ e μ { M k } , D denotes the upper entropy dimension of μ { M k } , D and dim q B Λ t denotes the quasi-Beurling dimension of Λ t .
In this...
