ON THE BOUNDEDNESS OF DUNKL-TYPE FRACTIONAL INTEGRAL OPERATOR IN THE GENERALIZED DUNKL-TYPE MORREY SPACES

Abstract

First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35