Some embeddings into the total Morrey spaces associated with the Dunkl operator on Rd

Abstract

. On the R d the Dunkl operators (cid:8) D k,j (cid:9) d j =1 are the differential-difference operators associated with the reflection group Z d 2 on R d . We study some embeddings into the total Morrey space ( D k - total Morrey space) L p,λ,µ ( µ k ) , 0 ≤ λ, µ < d + 2 γ k associated with the Dunkl operator on R d . These spaces generalize the Morrey spaces associated with the Dunkl operator on R d ( D k -Morrey space) so that L p,λ ( µ k ) ≡ L p,λ,λ ( µ k ) and the modified Morrey spaces associated with the Dunkl operator on R d (modified D k -Morrey space) so that (cid:101) L p,λ ( µ k ) ≡ L p,λ, 0 ( µ k ) .